Microlocal Analysis and Renormalization in Finite Temperature Field Theory

TL;DR

This paper revisits renormalization in finite temperature quantum field theory, clarifying the connection between zero and non-zero temperature divergences using microlocal analysis, and unifying different formalisms.

Contribution

It introduces a microlocal analysis approach to understand renormalization in FTFT, linking ultraviolet behavior at different temperatures and unifying formalism treatments.

Findings

Ultraviolet divergences are unaffected by temperature changes.

H"ormander's criterion clarifies distribution product existence in FTFT.

Unified treatment of imaginary and real time formalisms.

Abstract

We reassess the problem of renormalization in finite temperature field theory (FTFT). A new point of view elucidates the relation between the ultraviolet divergences for T=0 and $T \not= 0$ theories and makes clear the reason why the ultraviolet behavior keeps unaffected when we consider the FTFT version associated to a given quantum field theory (QFT). The strength of the derivation one lies on the H\"ormander's criterion for the existence of products of distributions in terms of the wavefront sets of the respective distributions. The approach allows us to regard the FTFT both imaginary and real time formalism at once in a unified way in the contour ordered formalism.