Covariant techniques in Quantum Field Theory

TL;DR

This paper reviews covariant techniques in quantum field theory, including background field gauge, zeta function regularization, and heat kernel methods, with detailed calculations of heat kernel coefficients.

Contribution

It provides a comprehensive review and detailed calculations of covariant techniques like heat kernel and zeta function regularization in quantum field theory.

Findings

Clarification of covariant computation methods

Explicit calculations of heat kernel coefficients

Enhanced understanding of regularization techniques

Abstract

In this paper some techniques useful to perform quantum field theory computations in a covariant manner are reviewed. In particular the background field gauge, the zeta function regularization and the heat kernel approach are highlighted. Some detailed calculations of the Schwinger-de Witt coefficients of the small proper time expansion of the heat kernel are also repeated in detail. This work reports lectures given by Enrique \'Alvarez at the IFT-UAM-CSIC in Madrid.