Gauge-Dependence of Green's Functions in QCD and QED

TL;DR

This paper investigates the gauge-dependence of Green's functions in QCD and QED, showing that while in QCD they cannot be directly derived in different gauges, in QED they can, under covariant gauge conditions.

Contribution

It clarifies the conditions under which Green's functions in QED and QCD can be related across different gauges, highlighting a fundamental difference between the two theories.

Findings

Green's functions in QCD are gauge-dependent and cannot be directly transformed between gauges.

In QED, Green's functions in covariant gauges are related and derivable across gauges.

The physical significance of gauge dependence differs between QCD and QED.

Abstract

When all Green's functions are known in a given gauge we may raise a question of whether it is possible or not to derive the corresponding ones in a different gauge. The answer is negative in QCD but affirmative in QED provided that we confine ourselves to the covariant gauge characterized by a gauge parameter $\alpha$. We shall discuss the physical significance of this conclusion.