#functionalrenormalizationgroup — Public Fediverse posts

#paperOfTheDay is "Perturbative renormalization and ifrared finiteness in the Wilson renormalization group: the massless scalar case" from 1993. The point of this paper is to prove renormalizability of massless scalar #quantumFieldTheory (which had been known for decades at that point) , but from a new perspective. Namely, instead of discussing the properties of #FeynmanIntegral s, the authors set up a set of integral equations for the quantum effective action in presence of UV and IR momentum cutoffs, and then show that the renormalized versions of these equations stay finite as either of the two cutoffs is removed, thus proving UV and IR finiteness of the renormalized theory.
Notice that this paper appeared in the early 1990s, at the same time as many foundational articles of the #functionalRenormalizationGroup , but the present article uses a custom derivation and a version of functional renormalization group that is not obviously equal to e.g. the Wetterich equation (although, as the authors discuss, it is a version of Polchinski's equation, and my impression is that all these functional renormalization group equations are to some extent equivalent up to changes of variables).
Regardless of whether renormalizability had been known, it is of course very important to check if an emergent new formulation of quantum field theory reproduces this result, or perhaps leads to new insights (or difficulties).
https://www.sciencedirect.com/science/article/abs/pii/S0370157321000156