Temperature Independent Renormalization of Finite Temperature Field Theory

TL;DR

This paper proves that finite temperature ^4 quantum field theory can be renormalized with temperature-independent counterterms using flow equations, confirming previous explicit calculations and ensuring consistent parameter flow with temperature.

Contribution

It provides a rigorous proof of temperature-independent renormalization in finite temperature ^4 theory using Wilson renormalization group methods, unlike traditional BPHZ approaches.

Findings

Counterterms can be chosen temperature independent.

The difference between T>0 and T=0 theories contains no relevant terms.

The approach allows simultaneous determination of renormalization conditions and counterterms.

Abstract

We analyse 4-dimensional massive $\vp^4$ theory at finite temperature T in the imaginary-time formalism. We present a rigorous proof that this quantum field theory is renormalizable, to all orders of the loop expansion. Our main point is to show that the counterterms can be chosen temperature independent, so that the temperature flow of the relevant parameters as a function of $T$ can be followed. Our result confirms the experience from explicit calculations to the leading orders. The proof is based on flow equations, i.e. on the (perturbative) Wilson renormalization group. In fact we will show that the difference between the theories at T>0 and at T=0 contains no relevant terms. Contrary to BPHZ type formalisms our approach permits to lay hand on renormalization conditions and counterterms at the same time, since both appear as boundary terms of the renormalization group flow. This is crucial for the proof.