  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.
