#quantumfieldtheory — Public Fediverse posts

https://www.europesays.com/ie/645560/ We May Already Have The First Hints of Quantum Gravity – Hiding in Plain Sight #AcceleratingExpansion #DarkEnergy #Éire #ExpansionRate #IE #Ireland #Physics #QuantumFieldTheory #QuantumMechanics #QuantumGravity #SavvasKoushiappas #Science #StandardCosmologicalModel

The #paperOfTheDay is "how to resum Feynman graphs" from 2013. In #quantumFieldTheory , #FeynmanIntegral s are the individual constituents of a perturbation expansion with respect to a small coupling parameter. Since the number of graphs grows factorially with their number of vertices, and (in Bosonic theories) these graphs all have the same sign, this perturbation series is divergent.
One can in some cases improve the situation by a Hubbard-Stratonovich transformation, or loop-vertex expansion. This is a rearrangement of the terms of the perturbation series with respect to a different parameter, such as the parameter 1/N (where N is large) in an O(N) symmetric theory. Morally, this amounts to a "perpendicular" summation: Fix a certain order in 1/N, and sum all orders in a small coupling.
The present article goes even further: The Feynman integral of a graph with E many edges consists of E! many "Hepp sectors", each given by a spanning tree of the graph. The proposal is to use these spanning trees as fundamental object, i.e. first fix a tree and compute the sum of all graphs where that tree contributes, and in a second step sum over all trees.
In the paper, this is envisoned somewhat schematically as an alternative way to compute the exact perturbation series. Today, #tropicalFieldTheory morally realizes this approach as a numerical sampling algorithm, where a Hepp sector is constructed as a primary object, and then any of the corresponding graphs is taken as a numerical sample. #physics
https://link.springer.com/article/10.1007/s00023-013-0299-8

The #paperOfTheDay is "how to resum Feynman graphs" from 2013. In #quantumFieldTheory , #FeynmanIntegral s are the individual constituents of a perturbation expansion with respect to a small coupling parameter. Since the number of graphs grows factorially with their number of vertices, and (in Bosonic theories) these graphs all have the same sign, this perturbation series is divergent.
One can in some cases improve the situation by a Hubbard-Stratonovich transformation, or loop-vertex expansion. This is a rearrangement of the terms of the perturbation series with respect to a different parameter, such as the parameter 1/N (where N is large) in an O(N) symmetric theory. Morally, this amounts to a "perpendicular" summation: Fix a certain order in 1/N, and sum all orders in a small coupling.
The present article goes even further: The Feynman integral of a graph with E many edges consists of E! many "Hepp sectors", each given by a spanning tree of the graph. The proposal is to use these spanning trees as fundamental object, i.e. first fix a tree and compute the sum of all graphs where that tree contributes, and in a second step sum over all trees.
In the paper, this is envisoned somewhat schematically as an alternative way to compute the exact perturbation series. Today, #tropicalFieldTheory morally realizes this approach as a numerical sampling algorithm, where a Hepp sector is constructed as a primary object, and then any of the corresponding graphs is taken as a numerical sample. #physics
https://link.springer.com/article/10.1007/s00023-013-0299-8

The #paperOfTheDay is "how to resum Feynman graphs" from 2013. In #quantumFieldTheory , #FeynmanIntegral s are the individual constituents of a perturbation expansion with respect to a small coupling parameter. Since the number of graphs grows factorially with their number of vertices, and (in Bosonic theories) these graphs all have the same sign, this perturbation series is divergent.
One can in some cases improve the situation by a Hubbard-Stratonovich transformation, or loop-vertex expansion. This is a rearrangement of the terms of the perturbation series with respect to a different parameter, such as the parameter 1/N (where N is large) in an O(N) symmetric theory. Morally, this amounts to a "perpendicular" summation: Fix a certain order in 1/N, and sum all orders in a small coupling.
The present article goes even further: The Feynman integral of a graph with E many edges consists of E! many "Hepp sectors", each given by a spanning tree of the graph. The proposal is to use these spanning trees as fundamental object, i.e. first fix a tree and compute the sum of all graphs where that tree contributes, and in a second step sum over all trees.
In the paper, this is envisoned somewhat schematically as an alternative way to compute the exact perturbation series. Today, #tropicalFieldTheory morally realizes this approach as a numerical sampling algorithm, where a Hepp sector is constructed as a primary object, and then any of the corresponding graphs is taken as a numerical sample. #physics
https://link.springer.com/article/10.1007/s00023-013-0299-8

The #paperOfTheDay is "how to resum Feynman graphs" from 2013. In #quantumFieldTheory , #FeynmanIntegral s are the individual constituents of a perturbation expansion with respect to a small coupling parameter. Since the number of graphs grows factorially with their number of vertices, and (in Bosonic theories) these graphs all have the same sign, this perturbation series is divergent.
One can in some cases improve the situation by a Hubbard-Stratonovich transformation, or loop-vertex expansion. This is a rearrangement of the terms of the perturbation series with respect to a different parameter, such as the parameter 1/N (where N is large) in an O(N) symmetric theory. Morally, this amounts to a "perpendicular" summation: Fix a certain order in 1/N, and sum all orders in a small coupling.
The present article goes even further: The Feynman integral of a graph with E many edges consists of E! many "Hepp sectors", each given by a spanning tree of the graph. The proposal is to use these spanning trees as fundamental object, i.e. first fix a tree and compute the sum of all graphs where that tree contributes, and in a second step sum over all trees.
In the paper, this is envisoned somewhat schematically as an alternative way to compute the exact perturbation series. Today, #tropicalFieldTheory morally realizes this approach as a numerical sampling algorithm, where a Hepp sector is constructed as a primary object, and then any of the corresponding graphs is taken as a numerical sample. #physics
https://link.springer.com/article/10.1007/s00023-013-0299-8

The #paperOfTheDay is "how to resum Feynman graphs" from 2013. In #quantumFieldTheory , #FeynmanIntegral s are the individual constituents of a perturbation expansion with respect to a small coupling parameter. Since the number of graphs grows factorially with their number of vertices, and (in Bosonic theories) these graphs all have the same sign, this perturbation series is divergent.
One can in some cases improve the situation by a Hubbard-Stratonovich transformation, or loop-vertex expansion. This is a rearrangement of the terms of the perturbation series with respect to a different parameter, such as the parameter 1/N (where N is large) in an O(N) symmetric theory. Morally, this amounts to a "perpendicular" summation: Fix a certain order in 1/N, and sum all orders in a small coupling.
The present article goes even further: The Feynman integral of a graph with E many edges consists of E! many "Hepp sectors", each given by a spanning tree of the graph. The proposal is to use these spanning trees as fundamental object, i.e. first fix a tree and compute the sum of all graphs where that tree contributes, and in a second step sum over all trees.
In the paper, this is envisoned somewhat schematically as an alternative way to compute the exact perturbation series. Today, #tropicalFieldTheory morally realizes this approach as a numerical sampling algorithm, where a Hepp sector is constructed as a primary object, and then any of the corresponding graphs is taken as a numerical sample. #physics
https://link.springer.com/article/10.1007/s00023-013-0299-8

The #paperOfTheDay is a classic in #mathematics from 1909: "Der Eulersche Dilogarithmus Und Seine Verallgemeinerungen" by Niels Nielsen. This article concerns generalizations of logarithms, in particular the dilogarithm. Starting from the fundamental identity
log(x) = integral from 1 to x of 1/t dt,
various authors had thought of "generalized logarithms" by integrating another time. One defines the dilogarithm
Li(x) = - integral from 0 to x of log(1-t)/t dt,
but many other generalizations are conceivable, for example why not allow some other rational function in place of 1/t in the integrand? This was answered by Hill and Kummer, who showed that if F and G are arbitrary rational functions, then any integral of F(t) log(G(t)) dt evaluates to a finite linear combination of Li(x) plus logarithms.
Nielsen gives a comprehensive review of known results about dilogarithms, remarking that notation and definitions in the existing literature are inconsistent and unnecessarily complicated.
In the second part of the article, one class of further generalizations is proposed, today known as "Nielsen polylogarithms", essentially integrals of log^(m-1)(t) log^p(1-t) for arbitrary positive integers m and p. These are truly more general than the dilogarithm.
Funnily, Nielsen starts his work by remarking that dilogarithms appear to be a rather unimportant class of functions, compared to elliptic integrals and hypergeometric functions which have plenty application in #physics . Of course, this changed 30 years later with the advent of #QuantumFieldTheory . Today, generalized polylogarithms are the most common class of special functions encountered in #FeynmanIntegral s.
https://katalog.bibliothek.kit.edu/bib/516451

The #paperOfTheDay is a classic in #mathematics from 1909: "Der Eulersche Dilogarithmus Und Seine Verallgemeinerungen" by Niels Nielsen. This article concerns generalizations of logarithms, in particular the dilogarithm. Starting from the fundamental identity
log(x) = integral from 1 to x of 1/t dt,
various authors had thought of "generalized logarithms" by integrating another time. One defines the dilogarithm
Li(x) = - integral from 0 to x of log(1-t)/t dt,
but many other generalizations are conceivable, for example why not allow some other rational function in place of 1/t in the integrand? This was answered by Hill and Kummer, who showed that if F and G are arbitrary rational functions, then any integral of F(t) log(G(t)) dt evaluates to a finite linear combination of Li(x) plus logarithms.
Nielsen gives a comprehensive review of known results about dilogarithms, remarking that notation and definitions in the existing literature are inconsistent and unnecessarily complicated.
In the second part of the article, one class of further generalizations is proposed, today known as "Nielsen polylogarithms", essentially integrals of log^(m-1)(t) log^p(1-t) for arbitrary positive integers m and p. These are truly more general than the dilogarithm.
Funnily, Nielsen starts his work by remarking that dilogarithms appear to be a rather unimportant class of functions, compared to elliptic integrals and hypergeometric functions which have plenty application in #physics . Of course, this changed 30 years later with the advent of #QuantumFieldTheory . Today, generalized polylogarithms are the most common class of special functions encountered in #FeynmanIntegral s.
https://katalog.bibliothek.kit.edu/bib/516451

The #paperOfTheDay is a classic in #mathematics from 1909: "Der Eulersche Dilogarithmus Und Seine Verallgemeinerungen" by Niels Nielsen. This article concerns generalizations of logarithms, in particular the dilogarithm. Starting from the fundamental identity
log(x) = integral from 1 to x of 1/t dt,
various authors had thought of "generalized logarithms" by integrating another time. One defines the dilogarithm
Li(x) = - integral from 0 to x of log(1-t)/t dt,
but many other generalizations are conceivable, for example why not allow some other rational function in place of 1/t in the integrand? This was answered by Hill and Kummer, who showed that if F and G are arbitrary rational functions, then any integral of F(t) log(G(t)) dt evaluates to a finite linear combination of Li(x) plus logarithms.
Nielsen gives a comprehensive review of known results about dilogarithms, remarking that notation and definitions in the existing literature are inconsistent and unnecessarily complicated.
In the second part of the article, one class of further generalizations is proposed, today known as "Nielsen polylogarithms", essentially integrals of log^(m-1)(t) log^p(1-t) for arbitrary positive integers m and p. These are truly more general than the dilogarithm.
Funnily, Nielsen starts his work by remarking that dilogarithms appear to be a rather unimportant class of functions, compared to elliptic integrals and hypergeometric functions which have plenty application in #physics . Of course, this changed 30 years later with the advent of #QuantumFieldTheory . Today, generalized polylogarithms are the most common class of special functions encountered in #FeynmanIntegral s.
https://katalog.bibliothek.kit.edu/bib/516451

The #paperOfTheDay is a classic in #mathematics from 1909: "Der Eulersche Dilogarithmus Und Seine Verallgemeinerungen" by Niels Nielsen. This article concerns generalizations of logarithms, in particular the dilogarithm. Starting from the fundamental identity
log(x) = integral from 1 to x of 1/t dt,
various authors had thought of "generalized logarithms" by integrating another time. One defines the dilogarithm
Li(x) = - integral from 0 to x of log(1-t)/t dt,
but many other generalizations are conceivable, for example why not allow some other rational function in place of 1/t in the integrand? This was answered by Hill and Kummer, who showed that if F and G are arbitrary rational functions, then any integral of F(t) log(G(t)) dt evaluates to a finite linear combination of Li(x) plus logarithms.
Nielsen gives a comprehensive review of known results about dilogarithms, remarking that notation and definitions in the existing literature are inconsistent and unnecessarily complicated.
In the second part of the article, one class of further generalizations is proposed, today known as "Nielsen polylogarithms", essentially integrals of log^(m-1)(t) log^p(1-t) for arbitrary positive integers m and p. These are truly more general than the dilogarithm.
Funnily, Nielsen starts his work by remarking that dilogarithms appear to be a rather unimportant class of functions, compared to elliptic integrals and hypergeometric functions which have plenty application in #physics . Of course, this changed 30 years later with the advent of #QuantumFieldTheory . Today, generalized polylogarithms are the most common class of special functions encountered in #FeynmanIntegral s.
https://katalog.bibliothek.kit.edu/bib/516451

The #paperOfTheDay is a classic in #mathematics from 1909: "Der Eulersche Dilogarithmus Und Seine Verallgemeinerungen" by Niels Nielsen. This article concerns generalizations of logarithms, in particular the dilogarithm. Starting from the fundamental identity
log(x) = integral from 1 to x of 1/t dt,
various authors had thought of "generalized logarithms" by integrating another time. One defines the dilogarithm
Li(x) = - integral from 0 to x of log(1-t)/t dt,
but many other generalizations are conceivable, for example why not allow some other rational function in place of 1/t in the integrand? This was answered by Hill and Kummer, who showed that if F and G are arbitrary rational functions, then any integral of F(t) log(G(t)) dt evaluates to a finite linear combination of Li(x) plus logarithms.
Nielsen gives a comprehensive review of known results about dilogarithms, remarking that notation and definitions in the existing literature are inconsistent and unnecessarily complicated.
In the second part of the article, one class of further generalizations is proposed, today known as "Nielsen polylogarithms", essentially integrals of log^(m-1)(t) log^p(1-t) for arbitrary positive integers m and p. These are truly more general than the dilogarithm.
Funnily, Nielsen starts his work by remarking that dilogarithms appear to be a rather unimportant class of functions, compared to elliptic integrals and hypergeometric functions which have plenty application in #physics . Of course, this changed 30 years later with the advent of #QuantumFieldTheory . Today, generalized polylogarithms are the most common class of special functions encountered in #FeynmanIntegral s.
https://katalog.bibliothek.kit.edu/bib/516451

АНТРОПОЛОГИЯ, ANTHROPOLOGY, АНТРОПОЛОГІЯ
#АНТРОПОЛОГИЯ, #ANTHROPOLOGY, #АНТРОПОЛОГІЯ
t.me/scilib_yura15cbx/542

Thermodynamics, statistical physics
Термодинамика, статистическая физика
Термодинаміка, статистична фізика
#Thermodynamics, #statistical physics
#Термодинамика, #статистическаяфизика
#Термодинаміка, #статистичнафізика
t.me/scilib_yura15cbx/541

PQm Quantum mechanics
Квантовая механика
Квантова механіка
#Quantum mechanics
#Квантоваямеханика
#Квантовамеханіка
t.me/scilib_yura15cbx/540

PQft Quantum field theory
Квантовая теория поля
Квантова теорія поля
#Quantum field theory
t.me/scilib_yura15cbx/539

Фазовые переходы
Phase_transitions, Фазовіпереходи
#Фазовые переходы
#Phase transitions, #Фазовіпереходи
t.me/scilib_yura15cbx/538

Пиротехника, Піротехніка, Pyrotechnics
#Пиротехника, #Піротехніка, #Pyrotechnics
t.me/scilib_yura15cbx/537

Астрономия, Астрономія, Astronomy
#Астрономия, #Астрономія, #Astronomy
t.me/scilib_yura15cbx/536

PPop Popular-level
Популярная физика
Популярна Фізика
t.me/scilib_yura15cbx/535

PG General courses
Общие курсы
Загальні курси
t.me/scilib_yura15cbx/534

PPl Plasma Плазма
Физика плазмы
#Plasma #Плазма
#Физика плазмы
t.me/scilib_yura15cbx/533

PPh Philosophy of Physics
Философия физики,
Філософія фізики
t.me/scilib_yura15cbx/532

POs Oscillations and waves
Колебания и волны
Коливання і хвилі
t.me/scilib_yura15cbx/531

PNu Nuclear Physics
Ядерна фізика
Ядерная физика
#Nuclear Physics
#Ядернафізика
#Ядернаяфизика
t.me/scilib_yura15cbx/530

PNc Nonlinear chaos
Нелинейный хаос
Нелінійний хаос
#Nonlinear chaos
#Нелинейныйхаос
#Нелінійнийхаос
t.me/scilib_yura15cbx/529

PM Atomic Molecular and Optical Physics
Атомна молекулярна та оптична Фізика
Атомная молекулярная и оптическая физика
t.me/scilib_yura15cbx/528

PGrc Cosmology
Космология
Космологія
#Cosmology
#Космология
#Космологія
t.me/scilib_yura15cbx/527

PGr Gravitation
Гравитация
Гравітація
#Gravitation
#Гравитация
#Гравітація
t.me/scilib_yura15cbx/526

PGe Encyclopaediae physics
Енциклопедія
Энциклопедии
t.me/scilib_yura15cbx/525

PE Electromagnetism
Електромагнетизм
Электромагнетизм
#Electromagnetism
#Електромагнетизм
#Электромагнетизм
t.me/scilib_yura15cbx/523

PD Dynamical systems
Динамические системы
Динамічна система
t.me/scilib_yura15cbx/522

PCh Chemical physics
Хімічна фізика
Химическая физика
#Chemical physics
#Хімічнафізика
#Химическаяфизика
t.me/scilib_yura15cbx/521

PCtm Theoretical mechanics
Теоретическая механика
Теоретична механіка
t.me/scilib_yura15cbx/520

PCstr Special relativity
Спеціальна теорія відносності
Специальная теория относительности
t.me/scilib_yura15cbx/519

PCft Classical fields
Классические поля, классическая теория поля, класична теорія поля
t.me/scilib_yura15cbx/518

АНТРОПОЛОГИЯ, ANTHROPOLOGY, АНТРОПОЛОГІЯ
#АНТРОПОЛОГИЯ, #ANTHROPOLOGY, #АНТРОПОЛОГІЯ
t.me/scilib_yura15cbx/542

Thermodynamics, statistical physics
Термодинамика, статистическая физика
Термодинаміка, статистична фізика
#Thermodynamics, #statistical physics
#Термодинамика, #статистическаяфизика
#Термодинаміка, #статистичнафізика
t.me/scilib_yura15cbx/541

PQm Quantum mechanics
Квантовая механика
Квантова механіка
#Quantum mechanics
#Квантоваямеханика
#Квантовамеханіка
t.me/scilib_yura15cbx/540

PQft Quantum field theory
Квантовая теория поля
Квантова теорія поля
#Quantum field theory
t.me/scilib_yura15cbx/539

Фазовые переходы
Phase_transitions, Фазовіпереходи
#Фазовые переходы
#Phase transitions, #Фазовіпереходи
t.me/scilib_yura15cbx/538

Пиротехника, Піротехніка, Pyrotechnics
#Пиротехника, #Піротехніка, #Pyrotechnics
t.me/scilib_yura15cbx/537

Астрономия, Астрономія, Astronomy
#Астрономия, #Астрономія, #Astronomy
t.me/scilib_yura15cbx/536

PPop Popular-level
Популярная физика
Популярна Фізика
t.me/scilib_yura15cbx/535

PG General courses
Общие курсы
Загальні курси
t.me/scilib_yura15cbx/534

PPl Plasma Плазма
Физика плазмы
#Plasma #Плазма
#Физика плазмы
t.me/scilib_yura15cbx/533

PPh Philosophy of Physics
Философия физики,
Філософія фізики
t.me/scilib_yura15cbx/532

POs Oscillations and waves
Колебания и волны
Коливання і хвилі
t.me/scilib_yura15cbx/531

PNu Nuclear Physics
Ядерна фізика
Ядерная физика
#Nuclear Physics
#Ядернафізика
#Ядернаяфизика
t.me/scilib_yura15cbx/530

PNc Nonlinear chaos
Нелинейный хаос
Нелінійний хаос
#Nonlinear chaos
#Нелинейныйхаос
#Нелінійнийхаос
t.me/scilib_yura15cbx/529

PM Atomic Molecular and Optical Physics
Атомна молекулярна та оптична Фізика
Атомная молекулярная и оптическая физика
t.me/scilib_yura15cbx/528

PGrc Cosmology
Космология
Космологія
#Cosmology
#Космология
#Космологія
t.me/scilib_yura15cbx/527

PGr Gravitation
Гравитация
Гравітація
#Gravitation
#Гравитация
#Гравітація
t.me/scilib_yura15cbx/526

PGe Encyclopaediae physics
Енциклопедія
Энциклопедии
t.me/scilib_yura15cbx/525

PE Electromagnetism
Електромагнетизм
Электромагнетизм
#Electromagnetism
#Електромагнетизм
#Электромагнетизм
t.me/scilib_yura15cbx/523

PD Dynamical systems
Динамические системы
Динамічна система
t.me/scilib_yura15cbx/522

PCh Chemical physics
Хімічна фізика
Химическая физика
#Chemical physics
#Хімічнафізика
#Химическаяфизика
t.me/scilib_yura15cbx/521

PCtm Theoretical mechanics
Теоретическая механика
Теоретична механіка
t.me/scilib_yura15cbx/520

PCstr Special relativity
Спеціальна теорія відносності
Специальная теория относительности
t.me/scilib_yura15cbx/519

PCft Classical fields
Классические поля, классическая теория поля, класична теорія поля
t.me/scilib_yura15cbx/518

АНТРОПОЛОГИЯ, ANTHROPOLOGY, АНТРОПОЛОГІЯ
#АНТРОПОЛОГИЯ, #ANTHROPOLOGY, #АНТРОПОЛОГІЯ
t.me/scilib_yura15cbx/542

Thermodynamics, statistical physics
Термодинамика, статистическая физика
Термодинаміка, статистична фізика
#Thermodynamics, #statistical physics
#Термодинамика, #статистическаяфизика
#Термодинаміка, #статистичнафізика
t.me/scilib_yura15cbx/541

PQm Quantum mechanics
Квантовая механика
Квантова механіка
#Quantum mechanics
#Квантоваямеханика
#Квантовамеханіка
t.me/scilib_yura15cbx/540

PQft Quantum field theory
Квантовая теория поля
Квантова теорія поля
#Quantum field theory
t.me/scilib_yura15cbx/539

Фазовые переходы
Phase_transitions, Фазовіпереходи
#Фазовые переходы
#Phase transitions, #Фазовіпереходи
t.me/scilib_yura15cbx/538

Пиротехника, Піротехніка, Pyrotechnics
#Пиротехника, #Піротехніка, #Pyrotechnics
t.me/scilib_yura15cbx/537

Астрономия, Астрономія, Astronomy
#Астрономия, #Астрономія, #Astronomy
t.me/scilib_yura15cbx/536

PPop Popular-level
Популярная физика
Популярна Фізика
t.me/scilib_yura15cbx/535

PG General courses
Общие курсы
Загальні курси
t.me/scilib_yura15cbx/534

PPl Plasma Плазма
Физика плазмы
#Plasma #Плазма
#Физика плазмы
t.me/scilib_yura15cbx/533

PPh Philosophy of Physics
Философия физики,
Філософія фізики
t.me/scilib_yura15cbx/532

POs Oscillations and waves
Колебания и волны
Коливання і хвилі
t.me/scilib_yura15cbx/531

PNu Nuclear Physics
Ядерна фізика
Ядерная физика
#Nuclear Physics
#Ядернафізика
#Ядернаяфизика
t.me/scilib_yura15cbx/530

PNc Nonlinear chaos
Нелинейный хаос
Нелінійний хаос
#Nonlinear chaos
#Нелинейныйхаос
#Нелінійнийхаос
t.me/scilib_yura15cbx/529

PM Atomic Molecular and Optical Physics
Атомна молекулярна та оптична Фізика
Атомная молекулярная и оптическая физика
t.me/scilib_yura15cbx/528

PGrc Cosmology
Космология
Космологія
#Cosmology
#Космология
#Космологія
t.me/scilib_yura15cbx/527

PGr Gravitation
Гравитация
Гравітація
#Gravitation
#Гравитация
#Гравітація
t.me/scilib_yura15cbx/526

PGe Encyclopaediae physics
Енциклопедія
Энциклопедии
t.me/scilib_yura15cbx/525

PE Electromagnetism
Електромагнетизм
Электромагнетизм
#Electromagnetism
#Електромагнетизм
#Электромагнетизм
t.me/scilib_yura15cbx/523

PD Dynamical systems
Динамические системы
Динамічна система
t.me/scilib_yura15cbx/522

PCh Chemical physics
Хімічна фізика
Химическая физика
#Chemical physics
#Хімічнафізика
#Химическаяфизика
t.me/scilib_yura15cbx/521

PCtm Theoretical mechanics
Теоретическая механика
Теоретична механіка
t.me/scilib_yura15cbx/520

PCstr Special relativity
Спеціальна теорія відносності
Специальная теория относительности
t.me/scilib_yura15cbx/519

PCft Classical fields
Классические поля, классическая теория поля, класична теорія поля
t.me/scilib_yura15cbx/518

АНТРОПОЛОГИЯ, ANTHROPOLOGY, АНТРОПОЛОГІЯ
#АНТРОПОЛОГИЯ, #ANTHROPOLOGY, #АНТРОПОЛОГІЯ
t.me/scilib_yura15cbx/542

Thermodynamics, statistical physics
Термодинамика, статистическая физика
Термодинаміка, статистична фізика
#Thermodynamics, #statistical physics
#Термодинамика, #статистическаяфизика
#Термодинаміка, #статистичнафізика
t.me/scilib_yura15cbx/541

PQm Quantum mechanics
Квантовая механика
Квантова механіка
#Quantum mechanics
#Квантоваямеханика
#Квантовамеханіка
t.me/scilib_yura15cbx/540

PQft Quantum field theory
Квантовая теория поля
Квантова теорія поля
#Quantum field theory
t.me/scilib_yura15cbx/539

Фазовые переходы
Phase_transitions, Фазовіпереходи
#Фазовые переходы
#Phase transitions, #Фазовіпереходи
t.me/scilib_yura15cbx/538

Пиротехника, Піротехніка, Pyrotechnics
#Пиротехника, #Піротехніка, #Pyrotechnics
t.me/scilib_yura15cbx/537

Астрономия, Астрономія, Astronomy
#Астрономия, #Астрономія, #Astronomy
t.me/scilib_yura15cbx/536

PPop Popular-level
Популярная физика
Популярна Фізика
t.me/scilib_yura15cbx/535

PG General courses
Общие курсы
Загальні курси
t.me/scilib_yura15cbx/534

PPl Plasma Плазма
Физика плазмы
#Plasma #Плазма
#Физика плазмы
t.me/scilib_yura15cbx/533

PPh Philosophy of Physics
Философия физики,
Філософія фізики
t.me/scilib_yura15cbx/532

POs Oscillations and waves
Колебания и волны
Коливання і хвилі
t.me/scilib_yura15cbx/531

PNu Nuclear Physics
Ядерна фізика
Ядерная физика
#Nuclear Physics
#Ядернафізика
#Ядернаяфизика
t.me/scilib_yura15cbx/530

PNc Nonlinear chaos
Нелинейный хаос
Нелінійний хаос
#Nonlinear chaos
#Нелинейныйхаос
#Нелінійнийхаос
t.me/scilib_yura15cbx/529

PM Atomic Molecular and Optical Physics
Атомна молекулярна та оптична Фізика
Атомная молекулярная и оптическая физика
t.me/scilib_yura15cbx/528

PGrc Cosmology
Космология
Космологія
#Cosmology
#Космология
#Космологія
t.me/scilib_yura15cbx/527

PGr Gravitation
Гравитация
Гравітація
#Gravitation
#Гравитация
#Гравітація
t.me/scilib_yura15cbx/526

PGe Encyclopaediae physics
Енциклопедія
Энциклопедии
t.me/scilib_yura15cbx/525

PE Electromagnetism
Електромагнетизм
Электромагнетизм
#Electromagnetism
#Електромагнетизм
#Электромагнетизм
t.me/scilib_yura15cbx/523

PD Dynamical systems
Динамические системы
Динамічна система
t.me/scilib_yura15cbx/522

PCh Chemical physics
Хімічна фізика
Химическая физика
#Chemical physics
#Хімічнафізика
#Химическаяфизика
t.me/scilib_yura15cbx/521

PCtm Theoretical mechanics
Теоретическая механика
Теоретична механіка
t.me/scilib_yura15cbx/520

PCstr Special relativity
Спеціальна теорія відносності
Специальная теория относительности
t.me/scilib_yura15cbx/519

PCft Classical fields
Классические поля, классическая теория поля, класична теорія поля
t.me/scilib_yura15cbx/518

АНТРОПОЛОГИЯ, ANTHROPOLOGY, АНТРОПОЛОГІЯ
#АНТРОПОЛОГИЯ, #ANTHROPOLOGY, #АНТРОПОЛОГІЯ
t.me/scilib_yura15cbx/542

Thermodynamics, statistical physics
Термодинамика, статистическая физика
Термодинаміка, статистична фізика
#Thermodynamics, #statistical physics
#Термодинамика, #статистическаяфизика
#Термодинаміка, #статистичнафізика
t.me/scilib_yura15cbx/541

PQm Quantum mechanics
Квантовая механика
Квантова механіка
#Quantum mechanics
#Квантоваямеханика
#Квантовамеханіка
t.me/scilib_yura15cbx/540

PQft Quantum field theory
Квантовая теория поля
Квантова теорія поля
#Quantum field theory
t.me/scilib_yura15cbx/539

Фазовые переходы
Phase_transitions, Фазовіпереходи
#Фазовые переходы
#Phase transitions, #Фазовіпереходи
t.me/scilib_yura15cbx/538

Пиротехника, Піротехніка, Pyrotechnics
#Пиротехника, #Піротехніка, #Pyrotechnics
t.me/scilib_yura15cbx/537

Астрономия, Астрономія, Astronomy
#Астрономия, #Астрономія, #Astronomy
t.me/scilib_yura15cbx/536

PPop Popular-level
Популярная физика
Популярна Фізика
t.me/scilib_yura15cbx/535

PG General courses
Общие курсы
Загальні курси
t.me/scilib_yura15cbx/534

PPl Plasma Плазма
Физика плазмы
#Plasma #Плазма
#Физика плазмы
t.me/scilib_yura15cbx/533

PPh Philosophy of Physics
Философия физики,
Філософія фізики
t.me/scilib_yura15cbx/532

POs Oscillations and waves
Колебания и волны
Коливання і хвилі
t.me/scilib_yura15cbx/531

PNu Nuclear Physics
Ядерна фізика
Ядерная физика
#Nuclear Physics
#Ядернафізика
#Ядернаяфизика
t.me/scilib_yura15cbx/530

PNc Nonlinear chaos
Нелинейный хаос
Нелінійний хаос
#Nonlinear chaos
#Нелинейныйхаос
#Нелінійнийхаос
t.me/scilib_yura15cbx/529

PM Atomic Molecular and Optical Physics
Атомна молекулярна та оптична Фізика
Атомная молекулярная и оптическая физика
t.me/scilib_yura15cbx/528

PGrc Cosmology
Космология
Космологія
#Cosmology
#Космология
#Космологія
t.me/scilib_yura15cbx/527

PGr Gravitation
Гравитация
Гравітація
#Gravitation
#Гравитация
#Гравітація
t.me/scilib_yura15cbx/526

PGe Encyclopaediae physics
Енциклопедія
Энциклопедии
t.me/scilib_yura15cbx/525

PE Electromagnetism
Електромагнетизм
Электромагнетизм
#Electromagnetism
#Електромагнетизм
#Электромагнетизм
t.me/scilib_yura15cbx/523

PD Dynamical systems
Динамические системы
Динамічна система
t.me/scilib_yura15cbx/522

PCh Chemical physics
Хімічна фізика
Химическая физика
#Chemical physics
#Хімічнафізика
#Химическаяфизика
t.me/scilib_yura15cbx/521

PCtm Theoretical mechanics
Теоретическая механика
Теоретична механіка
t.me/scilib_yura15cbx/520

PCstr Special relativity
Спеціальна теорія відносності
Специальная теория относительности
t.me/scilib_yura15cbx/519

PCft Classical fields
Классические поля, классическая теория поля, класична теорія поля
t.me/scilib_yura15cbx/518

Registration is still possible for the 13th International Conference on the exact #renormalization group, 1-5 September 2026 in Sussex, UK.
This #academicConference about the #FRG takes place every two years, and deals with #QuantumFieldTheory, critical phenomena, statsitical #physics and related topics.
https://indico.global/event/16125/overview

Registration is still possible for the 13th International Conference on the exact #renormalization group, 1-5 September 2026 in Sussex, UK.
This #academicConference about the #FRG takes place every two years, and deals with #QuantumFieldTheory, critical phenomena, statsitical #physics and related topics.
https://indico.global/event/16125/overview

Registration is still possible for the 13th International Conference on the exact #renormalization group, 1-5 September 2026 in Sussex, UK.
This #academicConference about the #FRG takes place every two years, and deals with #QuantumFieldTheory, critical phenomena, statsitical #physics and related topics.
https://indico.global/event/16125/overview

Registration is still possible for the 13th International Conference on the exact #renormalization group, 1-5 September 2026 in Sussex, UK.
This #academicConference about the #FRG takes place every two years, and deals with #QuantumFieldTheory, critical phenomena, statsitical #physics and related topics.
https://indico.global/event/16125/overview

Registration is still possible for the 13th International Conference on the exact #renormalization group, 1-5 September 2026 in Sussex, UK.
This #academicConference about the #FRG takes place every two years, and deals with #QuantumFieldTheory, critical phenomena, statsitical #physics and related topics.
https://indico.global/event/16125/overview

The #paperOfTheDay is "Landau's Leviathans" from 2026. This paper concerns scattering #amplitudes in #QuantumFieldTheory . Theser are computed through #FeynmanIntegral s, and they express the probability of a scattering event as a function of masses and momenta of all particles involved in the process. This functional dependence is very complicated, as can be seen already in much simpler theories: If one e.g. considers an idealized pendulum under the effect of an external oscillation, the behaviour strongly depends on the frequency of the external oscillation. If it coincides with the pendulum's natural ("eigen") frequency, the pendulum will swing strongly, otherwise rather not. A "response function", as a function of external frequency, therefore has a peak at this particular frequency.
In the same way, the scattering amplitude of quantum fields has all sorts of peaks and singularities when certain combinations of the energies of incoming particles match masses of particles. For practical calculations, it is useful to know when that happens. The present draft introduces a new method, based on algebraic geometry, to determine these points. In principle, this "only" amounts to simplifying or solving systems of polynomial equations with rational coefficients, but in practice this is hardly doable (a polynomial in multiple variables can have extremely many independent coefficients). So they do the actual computations over finite fields: Instead of dealing with huge rational numbers and functions, they compute everything modulo a prime so that all numbers fit into standard integer types, repeat this many times, and finally reconstruct the true rational function. #physics https://arxiv.org/abs/2606.29612

The #paperOfTheDay is "Landau's Leviathans" from 2026. This paper concerns scattering #amplitudes in #QuantumFieldTheory . Theser are computed through #FeynmanIntegral s, and they express the probability of a scattering event as a function of masses and momenta of all particles involved in the process. This functional dependence is very complicated, as can be seen already in much simpler theories: If one e.g. considers an idealized pendulum under the effect of an external oscillation, the behaviour strongly depends on the frequency of the external oscillation. If it coincides with the pendulum's natural ("eigen") frequency, the pendulum will swing strongly, otherwise rather not. A "response function", as a function of external frequency, therefore has a peak at this particular frequency.
In the same way, the scattering amplitude of quantum fields has all sorts of peaks and singularities when certain combinations of the energies of incoming particles match masses of particles. For practical calculations, it is useful to know when that happens. The present draft introduces a new method, based on algebraic geometry, to determine these points. In principle, this "only" amounts to simplifying or solving systems of polynomial equations with rational coefficients, but in practice this is hardly doable (a polynomial in multiple variables can have extremely many independent coefficients). So they do the actual computations over finite fields: Instead of dealing with huge rational numbers and functions, they compute everything modulo a prime so that all numbers fit into standard integer types, repeat this many times, and finally reconstruct the true rational function. #physics https://arxiv.org/abs/2606.29612

The #paperOfTheDay is "Landau's Leviathans" from 2026. This paper concerns scattering #amplitudes in #QuantumFieldTheory . Theser are computed through #FeynmanIntegral s, and they express the probability of a scattering event as a function of masses and momenta of all particles involved in the process. This functional dependence is very complicated, as can be seen already in much simpler theories: If one e.g. considers an idealized pendulum under the effect of an external oscillation, the behaviour strongly depends on the frequency of the external oscillation. If it coincides with the pendulum's natural ("eigen") frequency, the pendulum will swing strongly, otherwise rather not. A "response function", as a function of external frequency, therefore has a peak at this particular frequency.
In the same way, the scattering amplitude of quantum fields has all sorts of peaks and singularities when certain combinations of the energies of incoming particles match masses of particles. For practical calculations, it is useful to know when that happens. The present draft introduces a new method, based on algebraic geometry, to determine these points. In principle, this "only" amounts to simplifying or solving systems of polynomial equations with rational coefficients, but in practice this is hardly doable (a polynomial in multiple variables can have extremely many independent coefficients). So they do the actual computations over finite fields: Instead of dealing with huge rational numbers and functions, they compute everything modulo a prime so that all numbers fit into standard integer types, repeat this many times, and finally reconstruct the true rational function. #physics https://arxiv.org/abs/2606.29612

The #paperOfTheDay is "Landau's Leviathans" from 2026. This paper concerns scattering #amplitudes in #QuantumFieldTheory . Theser are computed through #FeynmanIntegral s, and they express the probability of a scattering event as a function of masses and momenta of all particles involved in the process. This functional dependence is very complicated, as can be seen already in much simpler theories: If one e.g. considers an idealized pendulum under the effect of an external oscillation, the behaviour strongly depends on the frequency of the external oscillation. If it coincides with the pendulum's natural ("eigen") frequency, the pendulum will swing strongly, otherwise rather not. A "response function", as a function of external frequency, therefore has a peak at this particular frequency.
In the same way, the scattering amplitude of quantum fields has all sorts of peaks and singularities when certain combinations of the energies of incoming particles match masses of particles. For practical calculations, it is useful to know when that happens. The present draft introduces a new method, based on algebraic geometry, to determine these points. In principle, this "only" amounts to simplifying or solving systems of polynomial equations with rational coefficients, but in practice this is hardly doable (a polynomial in multiple variables can have extremely many independent coefficients). So they do the actual computations over finite fields: Instead of dealing with huge rational numbers and functions, they compute everything modulo a prime so that all numbers fit into standard integer types, repeat this many times, and finally reconstruct the true rational function. #physics https://arxiv.org/abs/2606.29612

The #paperOfTheDay is "Landau's Leviathans" from 2026. This paper concerns scattering #amplitudes in #QuantumFieldTheory . Theser are computed through #FeynmanIntegral s, and they express the probability of a scattering event as a function of masses and momenta of all particles involved in the process. This functional dependence is very complicated, as can be seen already in much simpler theories: If one e.g. considers an idealized pendulum under the effect of an external oscillation, the behaviour strongly depends on the frequency of the external oscillation. If it coincides with the pendulum's natural ("eigen") frequency, the pendulum will swing strongly, otherwise rather not. A "response function", as a function of external frequency, therefore has a peak at this particular frequency.
In the same way, the scattering amplitude of quantum fields has all sorts of peaks and singularities when certain combinations of the energies of incoming particles match masses of particles. For practical calculations, it is useful to know when that happens. The present draft introduces a new method, based on algebraic geometry, to determine these points. In principle, this "only" amounts to simplifying or solving systems of polynomial equations with rational coefficients, but in practice this is hardly doable (a polynomial in multiple variables can have extremely many independent coefficients). So they do the actual computations over finite fields: Instead of dealing with huge rational numbers and functions, they compute everything modulo a prime so that all numbers fit into standard integer types, repeat this many times, and finally reconstruct the true rational function. #physics https://arxiv.org/abs/2606.29612

https://www.europesays.com/dk/130605/ Mirror Removal Mid-Reflection Spawns Infinite Photons, Oslo Physicists Show #DynamicCasimirEffect #HawkingRadiation #Norway #Oslo #Photon #QuantumFieldTheory #QuantumVacuum #SuperconductingCircuits #TruncatedPhoton #UniversityOfOslo

#paperOfTheDay is "Comparison between large-order estimates and perturbation series in a scalar field theory with Gaussian propagator" from 1978.
The perturbation series for small coupling in #quantumFieldTheory is usually divergent (because the theory with negative coupling describes different #physics and is not "smoothly" connected with the case of positive coupling). To obtain finite physical predictions for the positive coupling case, a #resummation is needed. In the 1970s and 1980s, the computational techniques were for the first time sufficient to reach, say, order 4 in perturbation series computed with #FeynmanDiagram s, and the question arose how to actually do the resummation in practice.
The present paper studies a model quantum field theory, where the propagator is exp(-p^2). This is not physically accurate, but it allows to compute perturbation series to very high order (order 8 here) because the #FeynmanIntegral s are easier. Secondly, one can carry out an #instanton calculation to determine the leading large-order growth. This allows to study whether or not the series coefficients match the expected growth rate, and how to use various different methods of resummation. In particular, the instanton analysis predicts the location and algebraic exponent for the leading singularity in the Borel plane, and this can be used as an additional input: Either, compute the Borel transform directly with a shifted-gamma function to account for the singularity, or make an ansatz of the type (known singularity)x(Pade approximant) for the Borel transformed function. The numerical data shows that this gives substantially higher accuracy for the resummation. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.17.2144

#paperOfTheDay is "Comparison between large-order estimates and perturbation series in a scalar field theory with Gaussian propagator" from 1978.
The perturbation series for small coupling in #quantumFieldTheory is usually divergent (because the theory with negative coupling describes different #physics and is not "smoothly" connected with the case of positive coupling). To obtain finite physical predictions for the positive coupling case, a #resummation is needed. In the 1970s and 1980s, the computational techniques were for the first time sufficient to reach, say, order 4 in perturbation series computed with #FeynmanDiagram s, and the question arose how to actually do the resummation in practice.
The present paper studies a model quantum field theory, where the propagator is exp(-p^2). This is not physically accurate, but it allows to compute perturbation series to very high order (order 8 here) because the #FeynmanIntegral s are easier. Secondly, one can carry out an #instanton calculation to determine the leading large-order growth. This allows to study whether or not the series coefficients match the expected growth rate, and how to use various different methods of resummation. In particular, the instanton analysis predicts the location and algebraic exponent for the leading singularity in the Borel plane, and this can be used as an additional input: Either, compute the Borel transform directly with a shifted-gamma function to account for the singularity, or make an ansatz of the type (known singularity)x(Pade approximant) for the Borel transformed function. The numerical data shows that this gives substantially higher accuracy for the resummation. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.17.2144

#paperOfTheDay is "Comparison between large-order estimates and perturbation series in a scalar field theory with Gaussian propagator" from 1978.
The perturbation series for small coupling in #quantumFieldTheory is usually divergent (because the theory with negative coupling describes different #physics and is not "smoothly" connected with the case of positive coupling). To obtain finite physical predictions for the positive coupling case, a #resummation is needed. In the 1970s and 1980s, the computational techniques were for the first time sufficient to reach, say, order 4 in perturbation series computed with #FeynmanDiagram s, and the question arose how to actually do the resummation in practice.
The present paper studies a model quantum field theory, where the propagator is exp(-p^2). This is not physically accurate, but it allows to compute perturbation series to very high order (order 8 here) because the #FeynmanIntegral s are easier. Secondly, one can carry out an #instanton calculation to determine the leading large-order growth. This allows to study whether or not the series coefficients match the expected growth rate, and how to use various different methods of resummation. In particular, the instanton analysis predicts the location and algebraic exponent for the leading singularity in the Borel plane, and this can be used as an additional input: Either, compute the Borel transform directly with a shifted-gamma function to account for the singularity, or make an ansatz of the type (known singularity)x(Pade approximant) for the Borel transformed function. The numerical data shows that this gives substantially higher accuracy for the resummation. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.17.2144

#paperOfTheDay is "Comparison between large-order estimates and perturbation series in a scalar field theory with Gaussian propagator" from 1978.
The perturbation series for small coupling in #quantumFieldTheory is usually divergent (because the theory with negative coupling describes different #physics and is not "smoothly" connected with the case of positive coupling). To obtain finite physical predictions for the positive coupling case, a #resummation is needed. In the 1970s and 1980s, the computational techniques were for the first time sufficient to reach, say, order 4 in perturbation series computed with #FeynmanDiagram s, and the question arose how to actually do the resummation in practice.
The present paper studies a model quantum field theory, where the propagator is exp(-p^2). This is not physically accurate, but it allows to compute perturbation series to very high order (order 8 here) because the #FeynmanIntegral s are easier. Secondly, one can carry out an #instanton calculation to determine the leading large-order growth. This allows to study whether or not the series coefficients match the expected growth rate, and how to use various different methods of resummation. In particular, the instanton analysis predicts the location and algebraic exponent for the leading singularity in the Borel plane, and this can be used as an additional input: Either, compute the Borel transform directly with a shifted-gamma function to account for the singularity, or make an ansatz of the type (known singularity)x(Pade approximant) for the Borel transformed function. The numerical data shows that this gives substantially higher accuracy for the resummation. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.17.2144

#paperOfTheDay is "Comparison between large-order estimates and perturbation series in a scalar field theory with Gaussian propagator" from 1978.
The perturbation series for small coupling in #quantumFieldTheory is usually divergent (because the theory with negative coupling describes different #physics and is not "smoothly" connected with the case of positive coupling). To obtain finite physical predictions for the positive coupling case, a #resummation is needed. In the 1970s and 1980s, the computational techniques were for the first time sufficient to reach, say, order 4 in perturbation series computed with #FeynmanDiagram s, and the question arose how to actually do the resummation in practice.
The present paper studies a model quantum field theory, where the propagator is exp(-p^2). This is not physically accurate, but it allows to compute perturbation series to very high order (order 8 here) because the #FeynmanIntegral s are easier. Secondly, one can carry out an #instanton calculation to determine the leading large-order growth. This allows to study whether or not the series coefficients match the expected growth rate, and how to use various different methods of resummation. In particular, the instanton analysis predicts the location and algebraic exponent for the leading singularity in the Borel plane, and this can be used as an additional input: Either, compute the Borel transform directly with a shifted-gamma function to account for the singularity, or make an ansatz of the type (known singularity)x(Pade approximant) for the Borel transformed function. The numerical data shows that this gives substantially higher accuracy for the resummation. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.17.2144

Registration is open for the #academicConference "High Precision for Hard Processes 2026) in #Karlsruhe Germany on 5-9 October 2026. This series of workshops is devoted to high-precision studies of hard scattering processes at hadron colliders and beyond. The main themes are recent developments and new results for theoretical computations in #quantumFieldTheory and their applications to collider phenomenology.
Abstracts need to be submitted before 15 July.
https://indico.kit.edu/event/5167/overview
#physics

Registration is open for the #academicConference "High Precision for Hard Processes 2026) in #Karlsruhe Germany on 5-9 October 2026. This series of workshops is devoted to high-precision studies of hard scattering processes at hadron colliders and beyond. The main themes are recent developments and new results for theoretical computations in #quantumFieldTheory and their applications to collider phenomenology.
Abstracts need to be submitted before 15 July.
https://indico.kit.edu/event/5167/overview
#physics

Registration is open for the #academicConference "High Precision for Hard Processes 2026) in #Karlsruhe Germany on 5-9 October 2026. This series of workshops is devoted to high-precision studies of hard scattering processes at hadron colliders and beyond. The main themes are recent developments and new results for theoretical computations in #quantumFieldTheory and their applications to collider phenomenology.
Abstracts need to be submitted before 15 July.
https://indico.kit.edu/event/5167/overview
#physics

Registration is open for the #academicConference "High Precision for Hard Processes 2026) in #Karlsruhe Germany on 5-9 October 2026. This series of workshops is devoted to high-precision studies of hard scattering processes at hadron colliders and beyond. The main themes are recent developments and new results for theoretical computations in #quantumFieldTheory and their applications to collider phenomenology.
Abstracts need to be submitted before 15 July.
https://indico.kit.edu/event/5167/overview
#physics

Registration is open for the #academicConference "High Precision for Hard Processes 2026) in #Karlsruhe Germany on 5-9 October 2026. This series of workshops is devoted to high-precision studies of hard scattering processes at hadron colliders and beyond. The main themes are recent developments and new results for theoretical computations in #quantumFieldTheory and their applications to collider phenomenology.
Abstracts need to be submitted before 15 July.
https://indico.kit.edu/event/5167/overview
#physics

#paperOfTheDay is "Effective five-wave Hamiltonian for surface water waves" from 1997. This article concerns (a certain idealization of) waves on the surface of deep water in one spacial dimension. These waves have a non-linear equation of motion, therefore they can "scatter" when they meet. This has nothing to do with #quantumFieldTheory , but still, the scattering amplitudes can be computed with #FeynmanDiagram s: The sum of all tree-level diagrams reproduces the non-quantum classical field theory. Such computation has the advantage that it is more structured, and ultimately simpler, than "manually" modifying and expanding the interaction Hamiltonian in superpositions of plane waves.
Since 1-dimensional water waves are not the most fashionable area of theoretical #physics right now, this work was maybe not widely known. However, it has resurfaced now as part of an ongoing effort trying to compute, or re-interpret, sums of tree-level Feynman diagrams (=non-quantum scattering amplitudes) in more geometric terms. While these endeavors in quantum field theory always have the shortcoming of leaving out the actual quantum part, for a classical field theory such as water waves, the sum of tree-level diagrams is a genuine physically relevant observable.
https://www.sciencedirect.com/science/article/pii/S0375960197002107?__cf_chl_f_tk=rgYKJNN8nI6263mmLkztzvasv.4l8IQQrTh0qPjse9Y-1783072682-1.0.1.1-BKQujlGYbuT1Onn9XcARc8fj7OS2.QuI8_CKS90K3dA

#paperOfTheDay is "Effective five-wave Hamiltonian for surface water waves" from 1997. This article concerns (a certain idealization of) waves on the surface of deep water in one spacial dimension. These waves have a non-linear equation of motion, therefore they can "scatter" when they meet. This has nothing to do with #quantumFieldTheory , but still, the scattering amplitudes can be computed with #FeynmanDiagram s: The sum of all tree-level diagrams reproduces the non-quantum classical field theory. Such computation has the advantage that it is more structured, and ultimately simpler, than "manually" modifying and expanding the interaction Hamiltonian in superpositions of plane waves.
Since 1-dimensional water waves are not the most fashionable area of theoretical #physics right now, this work was maybe not widely known. However, it has resurfaced now as part of an ongoing effort trying to compute, or re-interpret, sums of tree-level Feynman diagrams (=non-quantum scattering amplitudes) in more geometric terms. While these endeavors in quantum field theory always have the shortcoming of leaving out the actual quantum part, for a classical field theory such as water waves, the sum of tree-level diagrams is a genuine physically relevant observable.
https://www.sciencedirect.com/science/article/pii/S0375960197002107?__cf_chl_f_tk=rgYKJNN8nI6263mmLkztzvasv.4l8IQQrTh0qPjse9Y-1783072682-1.0.1.1-BKQujlGYbuT1Onn9XcARc8fj7OS2.QuI8_CKS90K3dA

#paperOfTheDay is "Effective five-wave Hamiltonian for surface water waves" from 1997. This article concerns (a certain idealization of) waves on the surface of deep water in one spacial dimension. These waves have a non-linear equation of motion, therefore they can "scatter" when they meet. This has nothing to do with #quantumFieldTheory , but still, the scattering amplitudes can be computed with #FeynmanDiagram s: The sum of all tree-level diagrams reproduces the non-quantum classical field theory. Such computation has the advantage that it is more structured, and ultimately simpler, than "manually" modifying and expanding the interaction Hamiltonian in superpositions of plane waves.
Since 1-dimensional water waves are not the most fashionable area of theoretical #physics right now, this work was maybe not widely known. However, it has resurfaced now as part of an ongoing effort trying to compute, or re-interpret, sums of tree-level Feynman diagrams (=non-quantum scattering amplitudes) in more geometric terms. While these endeavors in quantum field theory always have the shortcoming of leaving out the actual quantum part, for a classical field theory such as water waves, the sum of tree-level diagrams is a genuine physically relevant observable.
https://www.sciencedirect.com/science/article/pii/S0375960197002107?__cf_chl_f_tk=rgYKJNN8nI6263mmLkztzvasv.4l8IQQrTh0qPjse9Y-1783072682-1.0.1.1-BKQujlGYbuT1Onn9XcARc8fj7OS2.QuI8_CKS90K3dA

#paperOfTheDay is "Effective five-wave Hamiltonian for surface water waves" from 1997. This article concerns (a certain idealization of) waves on the surface of deep water in one spacial dimension. These waves have a non-linear equation of motion, therefore they can "scatter" when they meet. This has nothing to do with #quantumFieldTheory , but still, the scattering amplitudes can be computed with #FeynmanDiagram s: The sum of all tree-level diagrams reproduces the non-quantum classical field theory. Such computation has the advantage that it is more structured, and ultimately simpler, than "manually" modifying and expanding the interaction Hamiltonian in superpositions of plane waves.
Since 1-dimensional water waves are not the most fashionable area of theoretical #physics right now, this work was maybe not widely known. However, it has resurfaced now as part of an ongoing effort trying to compute, or re-interpret, sums of tree-level Feynman diagrams (=non-quantum scattering amplitudes) in more geometric terms. While these endeavors in quantum field theory always have the shortcoming of leaving out the actual quantum part, for a classical field theory such as water waves, the sum of tree-level diagrams is a genuine physically relevant observable.
https://www.sciencedirect.com/science/article/pii/S0375960197002107?__cf_chl_f_tk=rgYKJNN8nI6263mmLkztzvasv.4l8IQQrTh0qPjse9Y-1783072682-1.0.1.1-BKQujlGYbuT1Onn9XcARc8fj7OS2.QuI8_CKS90K3dA

#paperOfTheDay is "Effective five-wave Hamiltonian for surface water waves" from 1997. This article concerns (a certain idealization of) waves on the surface of deep water in one spacial dimension. These waves have a non-linear equation of motion, therefore they can "scatter" when they meet. This has nothing to do with #quantumFieldTheory , but still, the scattering amplitudes can be computed with #FeynmanDiagram s: The sum of all tree-level diagrams reproduces the non-quantum classical field theory. Such computation has the advantage that it is more structured, and ultimately simpler, than "manually" modifying and expanding the interaction Hamiltonian in superpositions of plane waves.
Since 1-dimensional water waves are not the most fashionable area of theoretical #physics right now, this work was maybe not widely known. However, it has resurfaced now as part of an ongoing effort trying to compute, or re-interpret, sums of tree-level Feynman diagrams (=non-quantum scattering amplitudes) in more geometric terms. While these endeavors in quantum field theory always have the shortcoming of leaving out the actual quantum part, for a classical field theory such as water waves, the sum of tree-level diagrams is a genuine physically relevant observable.
https://www.sciencedirect.com/science/article/pii/S0375960197002107?__cf_chl_f_tk=rgYKJNN8nI6263mmLkztzvasv.4l8IQQrTh0qPjse9Y-1783072682-1.0.1.1-BKQujlGYbuT1Onn9XcARc8fj7OS2.QuI8_CKS90K3dA

#paperOfTheDay is "The Diagrammar of Quantum Magnusian" from 2026.
The Magnusian is, morally, the logarithm of the S-matrix in #quantumFieldTheory . It has a perturbative expansion similarly to #FeynmanDiagrams , but these are not exactly the same diagrams, and they come with different combinatorial factors. The Magnus expansion has long been well understood for the case of differential equations, but the application to full quantum field theory is relatively new and so far had been rather ad-hoc, by expanding the corresponding series and explicitly matching terms. The present paper provides a systematic description of which diagrams, and with which combinatorial factors, appear in the Magnus expansion in QFT. Even for a scalar QFT, this is more complicated than ordinary Feynman diagrams, e.g. because the Magnus diagrams have directed edges (representing retarded propagators). https://arxiv.org/abs/2605.25473

#paperOfTheDay is "The Diagrammar of Quantum Magnusian" from 2026.
The Magnusian is, morally, the logarithm of the S-matrix in #quantumFieldTheory . It has a perturbative expansion similarly to #FeynmanDiagrams , but these are not exactly the same diagrams, and they come with different combinatorial factors. The Magnus expansion has long been well understood for the case of differential equations, but the application to full quantum field theory is relatively new and so far had been rather ad-hoc, by expanding the corresponding series and explicitly matching terms. The present paper provides a systematic description of which diagrams, and with which combinatorial factors, appear in the Magnus expansion in QFT. Even for a scalar QFT, this is more complicated than ordinary Feynman diagrams, e.g. because the Magnus diagrams have directed edges (representing retarded propagators). https://arxiv.org/abs/2605.25473

#paperOfTheDay is "The Diagrammar of Quantum Magnusian" from 2026.
The Magnusian is, morally, the logarithm of the S-matrix in #quantumFieldTheory . It has a perturbative expansion similarly to #FeynmanDiagrams , but these are not exactly the same diagrams, and they come with different combinatorial factors. The Magnus expansion has long been well understood for the case of differential equations, but the application to full quantum field theory is relatively new and so far had been rather ad-hoc, by expanding the corresponding series and explicitly matching terms. The present paper provides a systematic description of which diagrams, and with which combinatorial factors, appear in the Magnus expansion in QFT. Even for a scalar QFT, this is more complicated than ordinary Feynman diagrams, e.g. because the Magnus diagrams have directed edges (representing retarded propagators). https://arxiv.org/abs/2605.25473

#paperOfTheDay is "The Diagrammar of Quantum Magnusian" from 2026.
The Magnusian is, morally, the logarithm of the S-matrix in #quantumFieldTheory . It has a perturbative expansion similarly to #FeynmanDiagrams , but these are not exactly the same diagrams, and they come with different combinatorial factors. The Magnus expansion has long been well understood for the case of differential equations, but the application to full quantum field theory is relatively new and so far had been rather ad-hoc, by expanding the corresponding series and explicitly matching terms. The present paper provides a systematic description of which diagrams, and with which combinatorial factors, appear in the Magnus expansion in QFT. Even for a scalar QFT, this is more complicated than ordinary Feynman diagrams, e.g. because the Magnus diagrams have directed edges (representing retarded propagators). https://arxiv.org/abs/2605.25473

#paperOfTheDay is "The Magnus expansion in relativistic quantum field theory" from 2025.
One of the well-established ways to do computations in #quantumFieldTheory is perturbation theory in terms of #FeynmanIntegral s. From an analytic perspective, these integrals are the coefficients of a Dyson series, which is a power-series expansion of the time-evolution operator U (especially the S-matrix is a special case of U). This operator U is supposed to be unitary, so it seems plausible to write it as U=exp(i N) with some operator N, and to directly compute the quantity N. This is known as the #Magnus expansion, and has been rather well studied in the theory of differential equations in #mathematics . It has nice properties, in particular that even an inaccurate truncation of N still guarantees U to be unitary.
In recent years, the Magnus expansion has also received new attention in the field of scattering amplitudes in theoretical #physics . The present preprint concerns using Magnus expansions instead of Dyson series in perturbative quantum field theory. The series coefficients are distinct from Feynman integrals, but they have an analogous graphical representation, using retarded propagators in place of Feynman propagators, and slightly different #combinatorics on the corresponding #graphs . The paper contains excessively many examples which clearly indicate the general formulas, which are then stated (but not proved). Besides the actual application to future physics calculations, I think it could be an interesting project in #combinatorics to prove all these formulas, and relate them to the existing mathematical literature. https://arxiv.org/abs/2512.05017

#paperOfTheDay is "The Magnus expansion in relativistic quantum field theory" from 2025.
One of the well-established ways to do computations in #quantumFieldTheory is perturbation theory in terms of #FeynmanIntegral s. From an analytic perspective, these integrals are the coefficients of a Dyson series, which is a power-series expansion of the time-evolution operator U (especially the S-matrix is a special case of U). This operator U is supposed to be unitary, so it seems plausible to write it as U=exp(i N) with some operator N, and to directly compute the quantity N. This is known as the #Magnus expansion, and has been rather well studied in the theory of differential equations in #mathematics . It has nice properties, in particular that even an inaccurate truncation of N still guarantees U to be unitary.
In recent years, the Magnus expansion has also received new attention in the field of scattering amplitudes in theoretical #physics . The present preprint concerns using Magnus expansions instead of Dyson series in perturbative quantum field theory. The series coefficients are distinct from Feynman integrals, but they have an analogous graphical representation, using retarded propagators in place of Feynman propagators, and slightly different #combinatorics on the corresponding #graphs . The paper contains excessively many examples which clearly indicate the general formulas, which are then stated (but not proved). Besides the actual application to future physics calculations, I think it could be an interesting project in #combinatorics to prove all these formulas, and relate them to the existing mathematical literature. https://arxiv.org/abs/2512.05017

#paperOfTheDay is "The Magnus expansion in relativistic quantum field theory" from 2025.
One of the well-established ways to do computations in #quantumFieldTheory is perturbation theory in terms of #FeynmanIntegral s. From an analytic perspective, these integrals are the coefficients of a Dyson series, which is a power-series expansion of the time-evolution operator U (especially the S-matrix is a special case of U). This operator U is supposed to be unitary, so it seems plausible to write it as U=exp(i N) with some operator N, and to directly compute the quantity N. This is known as the #Magnus expansion, and has been rather well studied in the theory of differential equations in #mathematics . It has nice properties, in particular that even an inaccurate truncation of N still guarantees U to be unitary.
In recent years, the Magnus expansion has also received new attention in the field of scattering amplitudes in theoretical #physics . The present preprint concerns using Magnus expansions instead of Dyson series in perturbative quantum field theory. The series coefficients are distinct from Feynman integrals, but they have an analogous graphical representation, using retarded propagators in place of Feynman propagators, and slightly different #combinatorics on the corresponding #graphs . The paper contains excessively many examples which clearly indicate the general formulas, which are then stated (but not proved). Besides the actual application to future physics calculations, I think it could be an interesting project in #combinatorics to prove all these formulas, and relate them to the existing mathematical literature. https://arxiv.org/abs/2512.05017

#paperOfTheDay is "The Magnus expansion in relativistic quantum field theory" from 2025.
One of the well-established ways to do computations in #quantumFieldTheory is perturbation theory in terms of #FeynmanIntegral s. From an analytic perspective, these integrals are the coefficients of a Dyson series, which is a power-series expansion of the time-evolution operator U (especially the S-matrix is a special case of U). This operator U is supposed to be unitary, so it seems plausible to write it as U=exp(i N) with some operator N, and to directly compute the quantity N. This is known as the #Magnus expansion, and has been rather well studied in the theory of differential equations in #mathematics . It has nice properties, in particular that even an inaccurate truncation of N still guarantees U to be unitary.
In recent years, the Magnus expansion has also received new attention in the field of scattering amplitudes in theoretical #physics . The present preprint concerns using Magnus expansions instead of Dyson series in perturbative quantum field theory. The series coefficients are distinct from Feynman integrals, but they have an analogous graphical representation, using retarded propagators in place of Feynman propagators, and slightly different #combinatorics on the corresponding #graphs . The paper contains excessively many examples which clearly indicate the general formulas, which are then stated (but not proved). Besides the actual application to future physics calculations, I think it could be an interesting project in #combinatorics to prove all these formulas, and relate them to the existing mathematical literature. https://arxiv.org/abs/2512.05017

#paperOfTheDay is "The Magnus expansion in relativistic quantum field theory" from 2025.
One of the well-established ways to do computations in #quantumFieldTheory is perturbation theory in terms of #FeynmanIntegral s. From an analytic perspective, these integrals are the coefficients of a Dyson series, which is a power-series expansion of the time-evolution operator U (especially the S-matrix is a special case of U). This operator U is supposed to be unitary, so it seems plausible to write it as U=exp(i N) with some operator N, and to directly compute the quantity N. This is known as the #Magnus expansion, and has been rather well studied in the theory of differential equations in #mathematics . It has nice properties, in particular that even an inaccurate truncation of N still guarantees U to be unitary.
In recent years, the Magnus expansion has also received new attention in the field of scattering amplitudes in theoretical #physics . The present preprint concerns using Magnus expansions instead of Dyson series in perturbative quantum field theory. The series coefficients are distinct from Feynman integrals, but they have an analogous graphical representation, using retarded propagators in place of Feynman propagators, and slightly different #combinatorics on the corresponding #graphs . The paper contains excessively many examples which clearly indicate the general formulas, which are then stated (but not proved). Besides the actual application to future physics calculations, I think it could be an interesting project in #combinatorics to prove all these formulas, and relate them to the existing mathematical literature. https://arxiv.org/abs/2512.05017

#paperOfTheDay is "On the Local Borel transform of perturbation theory" from 2010. This article is about perturbative #QuantumFieldTheory , where one computes the terms of the perturbation series in terms of #FeynmanIntegral s. It is well known that the number of Feynman diagrams grows factorially with the loop order, and also there are individual classes of diagrams whose integral grows factorially. Since this is a growth rate faster than exponentially, it implies that the perturbation series does not converge.
For scalar quantum field theories in 2 or even 3 dimensions, this situation is relatively well under control because the second of the two effects is not present. In 4 dimensions, it is more tricky. It was established in the 1970s that at least the two effects do not conspire to give factorial-squared growth, but still, bounds were relatively crude. The present paper aims to give numerically more tight bounds of the magnitude of correlation functions depending on loop order, number of legs, or external momenta.
Notice that this statement is different from "Borel resummability": The latter asks whether the Borel transform is finite and not too quickly growing on the entire positive line, whereas the present article asks whether it has non-zero radius of convergence in the complex plane (e.g. bounded by singularities on the negative line).

Curiously, none of the existing articles, not even this present one, establish a factorial *lower* bound, i.e. from what is proven, it would be conceivable that the perturbation series is actually convergent. However, all numerical data we have is suggestive of factorial growth.
#physics
https://link.springer.com/article/10.1007/s00220-009-0979-x

#paperOfTheDay is "On the Local Borel transform of perturbation theory" from 2010. This article is about perturbative #QuantumFieldTheory , where one computes the terms of the perturbation series in terms of #FeynmanIntegral s. It is well known that the number of Feynman diagrams grows factorially with the loop order, and also there are individual classes of diagrams whose integral grows factorially. Since this is a growth rate faster than exponentially, it implies that the perturbation series does not converge.
For scalar quantum field theories in 2 or even 3 dimensions, this situation is relatively well under control because the second of the two effects is not present. In 4 dimensions, it is more tricky. It was established in the 1970s that at least the two effects do not conspire to give factorial-squared growth, but still, bounds were relatively crude. The present paper aims to give numerically more tight bounds of the magnitude of correlation functions depending on loop order, number of legs, or external momenta.
Notice that this statement is different from "Borel resummability": The latter asks whether the Borel transform is finite and not too quickly growing on the entire positive line, whereas the present article asks whether it has non-zero radius of convergence in the complex plane (e.g. bounded by singularities on the negative line).

Curiously, none of the existing articles, not even this present one, establish a factorial *lower* bound, i.e. from what is proven, it would be conceivable that the perturbation series is actually convergent. However, all numerical data we have is suggestive of factorial growth.
#physics
https://link.springer.com/article/10.1007/s00220-009-0979-x

#paperOfTheDay is "On the Local Borel transform of perturbation theory" from 2010. This article is about perturbative #QuantumFieldTheory , where one computes the terms of the perturbation series in terms of #FeynmanIntegral s. It is well known that the number of Feynman diagrams grows factorially with the loop order, and also there are individual classes of diagrams whose integral grows factorially. Since this is a growth rate faster than exponentially, it implies that the perturbation series does not converge.
For scalar quantum field theories in 2 or even 3 dimensions, this situation is relatively well under control because the second of the two effects is not present. In 4 dimensions, it is more tricky. It was established in the 1970s that at least the two effects do not conspire to give factorial-squared growth, but still, bounds were relatively crude. The present paper aims to give numerically more tight bounds of the magnitude of correlation functions depending on loop order, number of legs, or external momenta.
Notice that this statement is different from "Borel resummability": The latter asks whether the Borel transform is finite and not too quickly growing on the entire positive line, whereas the present article asks whether it has non-zero radius of convergence in the complex plane (e.g. bounded by singularities on the negative line).

Curiously, none of the existing articles, not even this present one, establish a factorial *lower* bound, i.e. from what is proven, it would be conceivable that the perturbation series is actually convergent. However, all numerical data we have is suggestive of factorial growth.
#physics
https://link.springer.com/article/10.1007/s00220-009-0979-x

#paperOfTheDay is "On the Local Borel transform of perturbation theory" from 2010. This article is about perturbative #QuantumFieldTheory , where one computes the terms of the perturbation series in terms of #FeynmanIntegral s. It is well known that the number of Feynman diagrams grows factorially with the loop order, and also there are individual classes of diagrams whose integral grows factorially. Since this is a growth rate faster than exponentially, it implies that the perturbation series does not converge.
For scalar quantum field theories in 2 or even 3 dimensions, this situation is relatively well under control because the second of the two effects is not present. In 4 dimensions, it is more tricky. It was established in the 1970s that at least the two effects do not conspire to give factorial-squared growth, but still, bounds were relatively crude. The present paper aims to give numerically more tight bounds of the magnitude of correlation functions depending on loop order, number of legs, or external momenta.
Notice that this statement is different from "Borel resummability": The latter asks whether the Borel transform is finite and not too quickly growing on the entire positive line, whereas the present article asks whether it has non-zero radius of convergence in the complex plane (e.g. bounded by singularities on the negative line).

Curiously, none of the existing articles, not even this present one, establish a factorial *lower* bound, i.e. from what is proven, it would be conceivable that the perturbation series is actually convergent. However, all numerical data we have is suggestive of factorial growth.
#physics
https://link.springer.com/article/10.1007/s00220-009-0979-x

#paperOfTheDay is "On the Local Borel transform of perturbation theory" from 2010. This article is about perturbative #QuantumFieldTheory , where one computes the terms of the perturbation series in terms of #FeynmanIntegral s. It is well known that the number of Feynman diagrams grows factorially with the loop order, and also there are individual classes of diagrams whose integral grows factorially. Since this is a growth rate faster than exponentially, it implies that the perturbation series does not converge.
For scalar quantum field theories in 2 or even 3 dimensions, this situation is relatively well under control because the second of the two effects is not present. In 4 dimensions, it is more tricky. It was established in the 1970s that at least the two effects do not conspire to give factorial-squared growth, but still, bounds were relatively crude. The present paper aims to give numerically more tight bounds of the magnitude of correlation functions depending on loop order, number of legs, or external momenta.
Notice that this statement is different from "Borel resummability": The latter asks whether the Borel transform is finite and not too quickly growing on the entire positive line, whereas the present article asks whether it has non-zero radius of convergence in the complex plane (e.g. bounded by singularities on the negative line).

Curiously, none of the existing articles, not even this present one, establish a factorial *lower* bound, i.e. from what is proven, it would be conceivable that the perturbation series is actually convergent. However, all numerical data we have is suggestive of factorial growth.
#physics
https://link.springer.com/article/10.1007/s00220-009-0979-x

Today's #paperoftheDay is all 3s: "3-loop 3PI effective action for 3D SU(3) QCD". The authors study quantum chromodynamics (#QCD, but without Fermions) in 3 Euclidean dimensions, but with an unconventional method: the 3PI effective action. These higher nPI effective actions in #quantumFieldTheory formally arise from higher-order Legendre transforms of W, the generating functional for connected correlation functions. The 1PI effective action, usually denoted gamma, is what is simply called "effective action" in most of the #physics literature, it is a functional of the classical field (i.e. the 1-point function of the quantum field theory). Analogously, a 3PI effective action is a functional of the 1-point, 2-point, and 3-point functions of the theory. This means that the true physical state of the theory coincides with the global minimum of the 3PI effective action with respect to these 3 functions (in the same way that a global minimum of the usual effective action is the true vacuum expectation value of the quantum field). Contrary to what one might think, the 3PI effective action is not the generating function for 3PI, i.e. 3-particle-irreducible, diagrams in a conventional sense, this choice of name is thus a bit unfortunate from a #graph theory perspective.
By nature, this method requires to work with momentum-dependent functions as "variables", not just a number like the (translation-invariant) field value for the 1PI action. This is handled in an interesting way: The authors use Pade approximants to parametrize these functions as a rational function, and the actual data they work with is the set of coefficients of these rational approximants.
https://arxiv.org/abs/1202.4756

Today's #paperoftheDay is all 3s: "3-loop 3PI effective action for 3D SU(3) QCD". The authors study quantum chromodynamics (#QCD, but without Fermions) in 3 Euclidean dimensions, but with an unconventional method: the 3PI effective action. These higher nPI effective actions in #quantumFieldTheory formally arise from higher-order Legendre transforms of W, the generating functional for connected correlation functions. The 1PI effective action, usually denoted gamma, is what is simply called "effective action" in most of the #physics literature, it is a functional of the classical field (i.e. the 1-point function of the quantum field theory). Analogously, a 3PI effective action is a functional of the 1-point, 2-point, and 3-point functions of the theory. This means that the true physical state of the theory coincides with the global minimum of the 3PI effective action with respect to these 3 functions (in the same way that a global minimum of the usual effective action is the true vacuum expectation value of the quantum field). Contrary to what one might think, the 3PI effective action is not the generating function for 3PI, i.e. 3-particle-irreducible, diagrams in a conventional sense, this choice of name is thus a bit unfortunate from a #graph theory perspective.
By nature, this method requires to work with momentum-dependent functions as "variables", not just a number like the (translation-invariant) field value for the 1PI action. This is handled in an interesting way: The authors use Pade approximants to parametrize these functions as a rational function, and the actual data they work with is the set of coefficients of these rational approximants.
https://arxiv.org/abs/1202.4756

Today's #paperoftheDay is all 3s: "3-loop 3PI effective action for 3D SU(3) QCD". The authors study quantum chromodynamics (#QCD, but without Fermions) in 3 Euclidean dimensions, but with an unconventional method: the 3PI effective action. These higher nPI effective actions in #quantumFieldTheory formally arise from higher-order Legendre transforms of W, the generating functional for connected correlation functions. The 1PI effective action, usually denoted gamma, is what is simply called "effective action" in most of the #physics literature, it is a functional of the classical field (i.e. the 1-point function of the quantum field theory). Analogously, a 3PI effective action is a functional of the 1-point, 2-point, and 3-point functions of the theory. This means that the true physical state of the theory coincides with the global minimum of the 3PI effective action with respect to these 3 functions (in the same way that a global minimum of the usual effective action is the true vacuum expectation value of the quantum field). Contrary to what one might think, the 3PI effective action is not the generating function for 3PI, i.e. 3-particle-irreducible, diagrams in a conventional sense, this choice of name is thus a bit unfortunate from a #graph theory perspective.
By nature, this method requires to work with momentum-dependent functions as "variables", not just a number like the (translation-invariant) field value for the 1PI action. This is handled in an interesting way: The authors use Pade approximants to parametrize these functions as a rational function, and the actual data they work with is the set of coefficients of these rational approximants.
https://arxiv.org/abs/1202.4756

Today's #paperoftheDay is all 3s: "3-loop 3PI effective action for 3D SU(3) QCD". The authors study quantum chromodynamics (#QCD, but without Fermions) in 3 Euclidean dimensions, but with an unconventional method: the 3PI effective action. These higher nPI effective actions in #quantumFieldTheory formally arise from higher-order Legendre transforms of W, the generating functional for connected correlation functions. The 1PI effective action, usually denoted gamma, is what is simply called "effective action" in most of the #physics literature, it is a functional of the classical field (i.e. the 1-point function of the quantum field theory). Analogously, a 3PI effective action is a functional of the 1-point, 2-point, and 3-point functions of the theory. This means that the true physical state of the theory coincides with the global minimum of the 3PI effective action with respect to these 3 functions (in the same way that a global minimum of the usual effective action is the true vacuum expectation value of the quantum field). Contrary to what one might think, the 3PI effective action is not the generating function for 3PI, i.e. 3-particle-irreducible, diagrams in a conventional sense, this choice of name is thus a bit unfortunate from a #graph theory perspective.
By nature, this method requires to work with momentum-dependent functions as "variables", not just a number like the (translation-invariant) field value for the 1PI action. This is handled in an interesting way: The authors use Pade approximants to parametrize these functions as a rational function, and the actual data they work with is the set of coefficients of these rational approximants.
https://arxiv.org/abs/1202.4756