Symmetry properties of massive gauge theories in nonlinear background gauges: Background dependence of Green functions

TL;DR

This paper investigates how Green functions in nonabelian gauge theories depend on nonlinear background fields, deriving relations that connect background-dependent and background-independent functionals, thus clarifying background influence on gauge theories.

Contribution

It derives a differential equation governing the background dependence of Green functions in nonlinear gauges and establishes explicit relations between background-dependent and background-independent functionals.

Findings

Background dependence of Green functions is fully characterized by a linear differential equation.

Relations between background-dependent and background-independent functionals are explicitly derived.

The results confirm previous findings in linear background gauges for physical Green functions.

Abstract

Nonabelian gauge theories with a generic background field A_mu in nonlinear gauges due to Delbourgo and Jarvis are investigated. The A_mu-dependence is completely determined by the help of a linear differential equation which obtaines from the Kluberg-Stern-Zuber and the Lee identity. Its integration leads to a relation between the one-particle irreducible vertex functional in the background field A_mu and the corresponding functional for A_mu = 0. An analogous relation holds for the generating functional of the complete Green functions which, after restriction to physical Green functions, is used to confirm a result obtained by Rouet in the case of linear background gauge.