Path-Integral Approach to Scale Anomaly at Finite Temperature

TL;DR

This paper derives the relativistic thermodynamic scale equation at finite temperature using path integrals and Fujikawa's method, linking the scale anomaly to measurable thermodynamic parameters in quantum field theory.

Contribution

It introduces a novel derivation of the scale anomaly at finite temperature using path integrals and provides a method to relate the beta function to thermodynamic measurements.

Findings

Derived the relativistic thermodynamic scale equation.

Applied Fujikawa's method with a matrix regulator.

Linked the beta function to macroscopic thermodynamic parameters.

Abstract

We derive the relativistic thermodynamic scale equation using imaginary-time path integrals, with complex scalar field theory taken as a concrete example. We use Fujikawa's method to derive the scaling anomaly for this system using a matrix regulator. We make a general scaling argument to show how for anomalous systems, the $\beta$ function of the vacuum theory can be derived from measurement of macroscopic thermodynamic parameters.