Gauge parameter dependence in gauge theories (revised: subsection 2.3)

TL;DR

This paper explores how gauge parameter dependence affects physical quantities in gauge theories and introduces an algebraic method using extended BRS transformations to control this dependence.

Contribution

It extends BRS transformations by incorporating gauge parameter variations into a Grassmann variable, providing an algebraic approach to gauge dependence.

Findings

Controlled gauge parameter dependence in various gauge theory quantities.

Applied method to anomaly coefficients, S-matrix elements, and renormalization group functions.

Demonstrated algebraic control over gauge dependence in theoretical calculations.

Abstract

Dependence on the gauge parameters is an important issue in gauge theories: physical quantities have to be independent. Extending BRS transformations by variation of the gauge parameter into a Grassmann variable one can control gauge parameter dependence algebraically. As application we discuss the anomaly coefficient in the Slavnov-Taylor identity, $S$-matrix elements, the vector two-point-function and the coefficients of renormalization group and Callan-Symanzik equation.