Connecting amplitudes in different gauges beyond perturbation theory: a canonical flow approach

TL;DR

This paper introduces a canonical flow method to compare gauge-dependent quantities in Yang-Mills theories beyond perturbation theory, ensuring gauge invariance of physical results.

Contribution

It develops a formalism based on canonical flow to relate Green's functions across different gauges beyond perturbation theory, explicitly solving Nielsen identities.

Findings

Explicit formulas for gauge dependence are derived.

Application to the gluon propagator demonstrates the method.

The approach links Landau gauge results to other gauges.

Abstract

Physical quantities in gauge theories have to be gauge-independent. However their evaluation can be greatly simplified by working in particular gauges. Since physical quantities have to be gauge invariant, it is important to establish an approach allowing the comparison of computations carried out in different gauges even beyond perturbation theory. We show that the dependence on the gauge parameter $\alpha=0$ in Yang-Mills theories is controlled by a canonical flow that explicitly solves the Nielsen identities of the model. Green's functions in the $\alpha=0$ gauge are given by amplitudes evaluated in the theory at $\alpha=0$ (e.g., in the example of Lorentz-covariant gauges, in terms of Landau gauge amplitudes) plus some contributions induced by the $\alpha=0$-dependence of the generating functional of the canonical flow. Explicit formulas are presented and an application of the formalism to the gluon propagator is discussed.