#paperoftheday — Public Fediverse posts

#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 "Theres' plenty of room in the middle: The unsung revolution of the renormalization group" from 2023 is a meta-article to commemorate 50 years of the #renormalization group in memory of one of its pioneers, Michael E. Fisher.
First of all, this article is a masterly and dense historical overview, basically every single reference in it is a breakthrough article worth reading. This being said, the article builds upon "Fisher's least cited article". There, Fisher introduces the thesis, which is elaborated in the present article, that almost all interesting #physics happens in the "middle"; concretely in the realm of collective phenomena and effective #fieldTheory governed by the renormalization group.
The present article discusses various examples, each with a provocative title, for example the BCS theory of superconductivity (famously a pure quantum effect) under the slogan that quantum mechanics is really not needed for condensed matter physics. The reasoning is: Such effects are described by effective field theories and "minimal models" with certain "asymptotic" properties (this is discussed in detail), in concrete cases these models can be derived from quantum mechanics, but this derivation does not really add anything to the practical understanding. At the same time, one can often obtain them from thermodynamic considerations alone, regardless of any more fundamental theory.
The article ends with the standard model of elementary particle physics, with the same thesis: One can view this as "just some EFT", which is valid as a very accurate model to describe observations, regardless of whether it is "fundamental"
. https://arxiv.org/abs/2306.06020v1

#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