Spectral functions and their applications

TL;DR

This paper introduces spectral functions like the heat kernel and zeta function, demonstrating their use in deriving high-temperature free energy asymptotics and analyzing chiral anomalies with boundary conditions.

Contribution

It provides an accessible overview of spectral functions and applies them to specific problems in quantum field theory, such as free energy asymptotics and chiral anomalies.

Findings

High temperature asymptotics of free energy derived

Chiral anomaly analyzed for MIT bag boundary conditions

Heat kernel and zeta function techniques applied successfully

Abstract

We give an introduction to the heat kernel technique and zeta function. Two applications are considered. First we derive the high temperature asymptotics of the free energy for boson fields in terms of the heat kernel expansion and zeta function. Another application is chiral anomaly for local (MIT bag) boundary conditions.