#amplitudes — Public Fediverse posts

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

Registration is open until 1st of June for the #amplitudes summer school in #Southampton UK. This school is targeted at doctoral candidates in theoretical #physics and it covers modern topics in #quantumFieldTheory and amplitudes at a level at detail exceeding the unsual university lectures. #academicConference
https://amplitudes.soton.ac.uk/school26/

Finally, in May there is the Higgs Centre School of Theoretical Physics in #Edinburgh . It is aimed at #phd students in theoretical #physics . Application deadline is 1 May, but accommodation subsidies will likely run out earlier. Topic this year are high energy scattering #amplitudes with two series of 5 x 2h lectures.

These were all of my conference announcements for today :-) .

https://indico.ph.ed.ac.uk/event/402/overview

In my #dailyPaperChallenge today I have read "Geometry-Kinematics Duality" from 2022. This article is about scalar field theories. From a structural point of view, the non-linear sigma model is the simplest possible scalar field theory, its Lagrangian consists solely of a kinematic term. From this, one can generate all other scalar Lagrangians by introducing a factor that is itself a functional of fields, i.e. it can act by multiplication, but also by derivatives or by "inverse derivatives". It turns out that this object can consistently be interpreted as a metric tensor, analogously to the metric tensor in general relativity, but acting on the "space of field variables" rather than "space of positions". With this, various tree level (i.e. classical, not quantum) #amplitudes can be expressed as geometric objects, for example the Riemann curvature tensor essentially takes the role of the 4-point amplitude. This paper is loosely related to my own work on field redefinition invariance from a few years ago. #paperOfTheDay https://arxiv.org/abs/2202.06972

 
#Scientists Discover a #Jewel at the Heart of #Quantum #Physics.

…"The #Amplituhedron looks like an intricate, multifaceted jewel in higher #dimensions. Encoded in its #volume are the most basic features of reality that can be calculated, “scattering amplitudes,” which represent the likelihood that a certain set of #particles will turn into certain other particles upon #colliding…

🔗 https://www.wired.com/2013/12/amplituhedron-jewel-quantum-physics/ 11 Dec 2013

#Community #TimeTravel #Research #quantum #amplitudes #math #geometry