Soft Dynamics and Gauge Theories

TL;DR

This paper introduces a method to eliminate soft divergences in gauge theories by dressing charged particles with gauge degrees of freedom, ensuring divergence-free Green's functions at all perturbation orders.

Contribution

It presents two fundamental equations derived from gauge invariance and velocity superselection rules to address infra-red divergences in gauge theories.

Findings

On-shell Green's functions are free of soft divergences in abelian theories.

The proposed dressing method is valid at all orders in perturbation theory.

New equations connect gauge invariance with velocity superselection in divergence removal.

Abstract

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.