#dailypaperchallenge — Public Fediverse posts

My #paperOfTheDay is the article "Asymptotically free solutions of the scalar mean field flow equations" from 2022. It concerns scalar #quantumFieldTheory . It is well known that the scalar phi^4 theory is "trivial" in 4 dimensions in the sense that if one imposes it at some high energy scale, then the interaction disappears at lower energy scales. This is different from e.g. quantum chromodynamics, which describes the strong force and is "asymptotically free": It can have non-vanishing interaction at low energy even if the high-energy theory is free.
This behaviour strongly depends on the particular interaction terms. In perturbation theory, one assumes that only the quartic phi^4vertex is present at high energy (because otherwise the perturbation series can not be renormalized). The method of #renormalization group flow equations, however, allows for an analysis of more general settings. The present article demonstrates that scalar field theories can have interesting, non-divergent, solutions even if they contain non-renormalizable interactions. #dailyPaperChallenge https://link.springer.com/article/10.1007/s00023-022-01194-w

My #paperOfTheDay for Friday was "The background field method and the non-linear sigma model" from 1988. It concerns #renormalization in theoretical #physics. In a theory with non-linear interactions, the observed quantities generally are in a non-linear relation with the "input parameters" (such as a coupling strength) of the theory. Hence, one can not immediately measure the input parameters. "Renormalization" is the procedure to disentangle these relations, so that one can use an experimentally measured value to determine parameters of the theory, and then predict all further observable outcomes (think of accelerating a ball that is immersed in water. From the required force, one can not immediately deduce the density or viscosity of water, but it is possible in principle after some calculations.). The "background field method" is one out of several approaches how to carry out renormalization in a field theory. In the present article, the authors demonstrate that this method can be used for the non-linear sigma model on an arbitrary curved surface, even if it is a bit more complicated herethan for other field theories that had been studied before. #dailyPaperChallenge https://doi.org/10.1016/0550-3213(88)90379-3

Today's #paperOfTheDay is "Why there is Nothing rather than something: A theory of the cosmological constant" from 1988. Like yesterday's paper, it deals with the intersection between quantum field theory and #generalRelativity, but the 30 years between them clearly show. Coleman's 1988 paper is an argument in the style of that time (which structurally is quite similar to much of the older #renormalon literature): Heuristic manipulations of formal objects such as the wave function of the universe, or divergent sums over all spacetime geometries. The outcome of this argument is that if #wormholes exist (caused by quantum effects at a scale that is much smaller than observations, but larger than the Planck scale), they can drive the cosmological constant to zero in an Euclidean path integral formulation of general relativity. As always with Coleman, the language is quite funny and frank about the paper's limitations: He writes "Although I find this theory in many ways very attractive, I must honestly stress its speculative character. It rests on wormhole dynamics and the Euclidean formulation of quantum gravity. This is doubly a house built on sand. [...] the Euclideon formulation of gravity is not a subject with firm foundations and clear rules of procedure; indeed, it is more like a trackless swamp". Observations like these have by now, 30 years later, led to a style of theoretical physics that is much more systematic and mathematical than in the 1980s, but also sometimes less intuitive. #dailyPaperChallenge https://doi.org/10.1016%2F0550-3213(88)90097-1

The #paperOfTheDay is "Renormalons and fixed points". This article from 1996 investigates the relation between #renormalons and infrared behaviour of #QCD. A renormalon is an effect that can lead to the divergence of a perturbation series, and such effects have been observed in various contexts. What has never become quite clear (at least to me) is the precise logical relation between its different incarnations: Divergence of the series, Landau poles, the peculiarities of QCD (renormalons exist in scalar theories as well!), non-trivial fixed points, and questions of uniqueness and resummability. The present paper points out some difficulties -- namely that some of the quantities involved are only defined perturbatively, or are sensitive to choices of analytic continuation. These considerations are interesting and not trivial, but I find it sometimes hard to follow the article since it has no explicit structure such as subsections or theorems, it is simply one continuous discussion. Or maybe I've just become too much of a mathematician by now.
#dailyPaperChallenge https://www.sciencedirect.com/science/article/pii/0370269396000615

A few days ago in the #dailyPaperChallenge I read Veneziano's proposal for a 4-point amplitude. This Friday, my #paperOfTheDay was "Alternative Construction of Crossing-Symmetric Amplitudes with Regge Behaviour" from 1969, were another, more general, expression is proposed by Virasoro. Overall, the spirit is very similar to Veneziaon's article: Propose a formula and discuss its properties. In particular, the Virasoro amplitude reduces to the Veneziano one if an extra condition is imposed, and at the same time it is argued that this condition is not satisfied for some realistic scattering processes, and therefore Virasoro's amplitude should be expected to better reflect reality than Veneziano's. Again, such heuristic arguments have become somewhat obsolete by now since we now know #QCD as a fundamental theory, and don't have to guess amplitudes any more. Still, the Virasoro amplitude stays relevant for certain theoretical considerations. https://journals.aps.org/pr/abstract/10.1103/PhysRev.177.2309

#paperOfTheDay for my #dailyPaperChallenge on Wednesday: "Graphical functions and single-valued multiple polylogarithms" from 2013. This is one of the foundational articles for the theory of graphical functions, a framework to compute a certain class of #FeynmanIntegral s in #physics They work for massless integrals that depend on two kinematical parameters (i.e. 3-point functions or confomral 4-point functions), and the key is to interpret these two parameters as a single complex number, and then use methods of complex analysis. Graphical functions are by far the most powerful method for computing such Feynman integrals, recently for example they are being used for the beta function of phi^4 theory at 8 loops. The paper is rather long, the section about single-valued multiple polylogarithms is actually a separate thing that isn't too relevant for graphical functions as such. https://arxiv.org/abs/1302.6445

#paperOfTheDay for Friday was "The Riemann Hypothesis: Past, Present and a Letter Through Time" from Thursday. The #Riemann hypothesis states that all non-trivial zeros of the Riemann zeta function have real part 1/2. Stated as a remark in Riemann's legendary paper 165years ago, it is by now one of the most well-known open problems in #mathematics. In the first half of the present paper, Connes gives a well-structured overview of several of the many relations, equivalent formulations, and consequences of the Riemann hypothesis. Very informative for the general (mathematically educated) reader! The second half describes one of the ongoing proof attempts in greater technical detail. #dailyPaperChallenge https://arxiv.org/abs/2602.04022

The #paperOfTheDay for my #dailyPaperChallenge is "on the theory of superconductivity" from 1950. At that time, it was not understood which physical mechanism causes superconductivity, so Ginzburg and Landau constructed a phenomenological theory: There must be some sort of superconducting charge carriers, therefore, they introduced a "density field" for those. From experimental findings, one has that it vanishes when the material becomes too hot, it is negatively affected by magnetic fields, and it can only support a finite amount of current. Using this as input, one can make an ansatz for the laws governing the charge density field, and this produces meaningful predictions for the behaviour of #superconductors. Nowadays, the BCS theory gives a more systematic description of (certain) superconductors, but Ginzburg-Landau theory has found many applications in other fields apart from superconductivity because the construction works whenever one does not know the precise laws governing microscopic constituents, but one has information about the observed large-scale properties.
https://www.sciencedirect.com/science/chapter/edited-volume/abs/pii/B978008010586450078X?via%3Dihub

My #paperOfTheDay is "Event generation with exponential scaling in multiplicity using AmpliCol" https://arxiv.org/abs/2601.19483 . Scattering experiments of elementary particles, e.g. at CERN, are very complicated even beyond the "core" physical process, for example the detectors can only measure in certain angles and with certain thresholds. To calibrate them, one needs to simulate the whole processes numerically, which is done with Monte Carlo methods. Among other things, the behaviour of particles in quantum chromodynamics depends on their "color", which is a type of charge somewhat analogous to electrical charge. Since that dependence is very complicated, the idea of the present paper is to use a simplified "leading" color-dependence as a proxy for importance sampling in the Monte Carlo simulation. This is analogous, but for a totally different physical question, to the weighting of individual random #FeynmanGraph s that I did in my "Predicting Feynman Periods" paper a while ago. https://link.springer.com/article/10.1007/JHEP11(2024)038 #dailyPaperChallenge

Today in the #dailyPaperChallenge I read (parts of) "critical \( \phi^4_{3,\epsilon} \)" from 2002. This paper deals with the #renormalization of a quartic interacting #fieldTheory in 3 dimensions, but with a non-standard (long-range) propagator \(1/p^{\frac 3 2} \). The methods they use are quite different from what I am accustomed to, but there are two points of contact with my work: Firstly, this theory is an example of a marginally coupled \(\phi^4 \) theory with non-integer propagator power. The #tropicalFieldTheory we are currently developing is also of that type. And secondly, the algebraic/combinatorial operations they use seem to fit nicely into a Hopf algebra description a la Connes-Kreimer (probably, someone has already worked that out in the 20 years since). Besides that, this paper also includes one section that is just a sequence of 24 lemmas, which would be more typical for Wittgenstein's tractatus than for a physics paper. What I also liked was that the paragraphs have individual titles, which makes the structure of arguments very easy to follow. https://link.springer.com/article/10.1007/s00220-003-0895-4

Today in the #dailyPaperChallenge I read (parts of) "critical \( \phi^4_{3,\epsilon} \)" from 2002. This paper deals with the #renormalization of a quartic interacting #fieldTheory in 3 dimensions, but with a non-standard (long-range) propagator \(1/p^{\frac 3 2} \). The methods they use are quite different from what I am accustomed to, but there are two points of contact with my work: Firstly, this theory is an example of a marginally coupled \(\phi^4 \) theory with non-integer propagator power. The #tropicalFieldTheory we are currently developing is also of that type. And secondly, the algebraic/combinatorial operations they use seem to fit nicely into a Hopf algebra description a la Connes-Kreimer (probably, someone has already worked that out in the 20 years since). Besides that, this paper also includes one section that is just a sequence of 24 lemmas, which would be more typical for Wittgenstein's tractatus than for a physics paper. What I also liked was that the paragraphs have individual titles, which makes the structure of arguments very easy to follow. https://link.springer.com/article/10.1007/s00220-003-0895-4

Today in the #dailyPaperChallenge I read (parts of) "critical \( \phi^4_{3,\epsilon} \)" from 2002. This paper deals with the #renormalization of a quartic interacting #fieldTheory in 3 dimensions, but with a non-standard (long-range) propagator \(1/p^{\frac 3 2} \). The methods they use are quite different from what I am accustomed to, but there are two points of contact with my work: Firstly, this theory is an example of a marginally coupled \(\phi^4 \) theory with non-integer propagator power. The #tropicalFieldTheory we are currently developing is also of that type. And secondly, the algebraic/combinatorial operations they use seem to fit nicely into a Hopf algebra description a la Connes-Kreimer (probably, someone has already worked that out in the 20 years since). Besides that, this paper also includes one section that is just a sequence of 24 lemmas, which would be more typical for Wittgenstein's tractatus than for a physics paper. What I also liked was that the paragraphs have individual titles, which makes the structure of arguments very easy to follow. https://link.springer.com/article/10.1007/s00220-003-0895-4

Today in the #dailyPaperChallenge I read (parts of) "critical \( \phi^4_{3,\epsilon} \)" from 2002. This paper deals with the #renormalization of a quartic interacting #fieldTheory in 3 dimensions, but with a non-standard (long-range) propagator \(1/p^{\frac 3 2} \). The methods they use are quite different from what I am accustomed to, but there are two points of contact with my work: Firstly, this theory is an example of a marginally coupled \(\phi^4 \) theory with non-integer propagator power. The #tropicalFieldTheory we are currently developing is also of that type. And secondly, the algebraic/combinatorial operations they use seem to fit nicely into a Hopf algebra description a la Connes-Kreimer (probably, someone has already worked that out in the 20 years since). Besides that, this paper also includes one section that is just a sequence of 24 lemmas, which would be more typical for Wittgenstein's tractatus than for a physics paper. What I also liked was that the paragraphs have individual titles, which makes the structure of arguments very easy to follow. https://link.springer.com/article/10.1007/s00220-003-0895-4

Today in the #dailyPaperChallenge I read (parts of) "critical \( \phi^4_{3,\epsilon} \)" from 2002. This paper deals with the #renormalization of a quartic interacting #fieldTheory in 3 dimensions, but with a non-standard (long-range) propagator \(1/p^{\frac 3 2} \). The methods they use are quite different from what I am accustomed to, but there are two points of contact with my work: Firstly, this theory is an example of a marginally coupled \(\phi^4 \) theory with non-integer propagator power. The #tropicalFieldTheory we are currently developing is also of that type. And secondly, the algebraic/combinatorial operations they use seem to fit nicely into a Hopf algebra description a la Connes-Kreimer (probably, someone has already worked that out in the 20 years since). Besides that, this paper also includes one section that is just a sequence of 24 lemmas, which would be more typical for Wittgenstein's tractatus than for a physics paper. What I also liked was that the paragraphs have individual titles, which makes the structure of arguments very easy to follow. https://link.springer.com/article/10.1007/s00220-003-0895-4

For my #dailyPaperChallenge , today I read "Rationalizability of square roots". This paper is about a problem one often faces in #FeynmanIntegral s in theoretical #physics: The integrand might be mostly rational, but contain a square root of some rational function R in several variables. Integrating square roots is not nice, so the idea is: can I find a rational change of variables such that R=P^2, where P is a rational function? If that is possible, the square root of R is simply replaced by P and the integral becomes much easier. If the rational functions are in only one variable, the answer is relatively simple, it works when the degree of the square-free factor is at most 2. For functions in several variables, this is increasingly more complicated and can be tackled with methods of algebraic geometry. https://doi.org/10.1016/j.jsc.2020.12.002