Spectral Functions in QFT

TL;DR

This paper provides a pedagogical overview of functional methods in quantum field theory, including heat-kernel and zeta-function techniques, applied to phenomena like the Casimir effect, pair production, finite temperature fields, and noncommutative theories.

Contribution

It introduces and explains the use of heat-kernel and zeta-function methods in various quantum field theory applications, including recent developments in noncommutative theories.

Findings

Analysis of Casimir effect using spectral functions

Application of spectral methods to pair production and finite temperature fields

Discussion of UV/IR mixing in noncommutative quantum field theories

Abstract

We present a pedagogical exposition of some applications of functional methods in quantum field theory: we use heat-kernel and zeta-function techniques to study the Casimir effect, the pair production in strong electric fields, quantum fields at finite temperature and beta-functions for a self-interacting scalar field, QED and pure Yang-Mills theories. The more recent application to the UV/IR mixing phenomenon in noncommutative theories is also discussed in this framework.