Gauge dependence of Green’s functions in 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 α. We shall discuss the physical significance of this conclusion.

Condition for confinement in non-Abelian gauge theories

“…Using the approaches developed in [2,3] and [4][5][6][7][8], we were able to give a rigorous proof of confinement for non-Abelian gauge theories in four dimensions as a consequence of the BRST invariance and the asymptotic freedom. Our results are based on the exact solutions obtained in [24] for the correlation functions.…”

“…In this section we present the approach to confinement proposed in [4][5][6][7][8] and show how this reduces to the Kugo-Ojima criterion [3]. We emphasize that our proof is for the theory without fermions.…”

“…Here σ 0 is an integration constant having the dimension of mass. It is easy to see how this propagator recovers asymptotic freedom [4][5][6][7][8]. In the high-energy limit, we make the momenta run to infinity.…”

“…For example, Kugo and Ojima proposed a condition from BRST invariance based on charge annihilation [2,3]. On a similar ground, Nishijima and collaborators [4][5][6][7][8] obtained a constraint on the amplitudes of unphysical states signaling confinement. These authors showed that colour confinement arises as a consequence of BRST invariance and asymptotic freedom.…”

“…In this paper, we will apply the condition derived in [4][5][6][7][8], reducing it to the case of the Kugo-Ojima criterion [3], when, for a non-Abelian gauge theory without fermions, we start with known exact solutions to solve it [24]. In this way, the propagators of the theory are known and we can evaluate the behavior of the poles.…”