Semiclassical thermodynamics of scalar fields

TL;DR

This paper develops a systematic semiclassical method to compute the finite-temperature partition function for scalar fields, involving classical solutions and Gaussian resummation of fluctuations, which is shown to be renormalizable.

Contribution

It introduces a new semiclassical approach for scalar field thermodynamics that simplifies calculations via classical solutions and Gaussian resummation, ensuring renormalizability.

Findings

Partition function expressed through classical solutions and differential equations.

Method is renormalizable with standard 1-loop counterterms.

Provides a systematic framework for scalar field thermodynamics.

Abstract

We present a systematic semiclassical procedure to compute the partition function for scalar field theories at finite temperature. The central objects in our scheme are the solutions of the classical equations of motion in imaginary time, with spatially independent boundary conditions. Field fluctuations -- both field deviations around these classical solutions, and fluctuations of the boundary value of the fields -- are resummed in a Gaussian approximation. In our final expression for the partition function, this resummation is reduced to solving certain ordinary differential equations. Moreover, we show that it is renormalizable with the usual 1-loop counterterms.