Gluon mass generation in the massless bound-state formalism

TL;DR

This paper provides a comprehensive all-order analysis of gluon mass generation using the massless bound-state formalism, linking it to the Schwinger mechanism and Bethe-Salpeter equations, and demonstrating its equivalence to the standard Schwinger-Dyson approach.

Contribution

It introduces a detailed formalism connecting gluon mass to bound-state formation and proves its equivalence to the traditional Schwinger-Dyson framework.

Findings

Gluon mass generation is governed by a Bethe-Salpeter equation.

The formalism relates the gluon mass to bound-state wave-functions.

The approach is equivalent to the standard Schwinger-Dyson method.

Abstract

We present a detailed, all-order study of gluon mass generation within the massless bound-state formalism, which constitutes the general framework for the systematic implementation of the Schwinger mechanism in non-Abelian gauge theories. The main ingredient of this formalism is the dynamical formation of bound-states with vanishing mass, which give rise to effective vertices containing massless poles; these latter vertices, in turn, trigger the Schwinger mechanism, and allow for the gauge-invariant generation of an effective gluon mass. This particular approach has the conceptual advantage of relating the gluon mass directly to quantities that are intrinsic to the bound-state formation itself, such as the "transition amplitude" and the corresponding "bound-state wave-function". As a result, the dynamical evolution of the gluon mass is largely determined by a Bethe-Salpeter equation that controls the dynamics of the relevant wave-function, rather than the Schwinger-Dyson equation of the gluon propagator, as happens in the standard treatment. The precise structure and field-theoretic properties of the transition amplitude are scrutinized in a variety of independent ways. In particular, a parallel study within the linear covariant (Landau) gauge and the background-field method reveals that a powerful identity, known to be valid at the level of conventional Green's functions, relates also the background and quantum transition amplitudes. Despite the differences in the ingredients and terminology employed, the massless bound-state formalism is absolutely equivalent to the standard approach based on Schwinger-Dyson equations. In fact, a set of powerful relations allow one to demonstrate the exact coincidence of the integral equations governing the momentum evolution of the gluon mass in both frameworks.