  Infra-red divergences obscure the underlying soft dynamics in gauge theories.
They remove the pole structures associated with particle propagation in the
various Green's functions of gauge theories. Here we present a solution to this
problem. We give two equations which describe how charged particles must be
dressed by gauge degrees of freedom. One follows from gauge invariance, the
other, which is new, from velocity superselection rules familiar from the heavy
quark effective theory. The solution to these equations in the abelian theory
is proven to lead to on-shell Green's functions that are free of soft
divergences at all orders in perturbation theory.
