Canonical Flow in the Space of Gauge Parameters

TL;DR

This paper demonstrates that gauge dependence in SU(N) Yang-Mills theory can be understood as a canonical flow driven by the extended Slavnov-Taylor identity, providing a systematic way to analyze gauge parameter variations.

Contribution

It introduces a canonical flow framework for gauge dependence in Yang-Mills theory, linking it to the extended Slavnov-Taylor identity and BRST symmetry transformations.

Findings

Analytic expansion of 1-PI amplitudes in gauge parameter

Expression of amplitudes in terms of Landau gauge coefficients

Application to the gauge flow of the gluon propagator

Abstract

Gauge dependence of one-particle irreducible (1-PI) amplitudes in SU(N) Yang-Mills theory is shown to be generated by a canonical flow with respect to (w.r.t.) the extended Slavnov-Taylor (ST) identity, induced by the transformation of the gauge parameter under the BRST symmetry. For linear covariant gauges, the analytic expansion in the gauge parameter of 1-PI amplitudes is given in terms of coefficients evaluated in the Landau gauge and of derivatives w.r.t. the gauge parameter of the generating functional of the flow. An application to the gauge flow of the gluon propagator is considered.