Construction of asymptotic fields for a charged particle

TL;DR

This paper constructs a new asymptotic field for charged particles in QED to address the non-existence issue caused by massless particles, enabling better analysis of scattering processes.

Contribution

It introduces a novel method to construct asymptotic fields with proper singularities for charged particles in theories with massless fields, specifically in QED.

Findings

Successfully constructs a charged particle field with correct momentum space singularities.

Addresses the non-existence problem of asymptotic fields in theories with massless particles.

Provides a framework applicable to quantum electrodynamics for improved scattering analysis.

Abstract

Asymptotic fields do not exist in theories with massless particles and fields, because the vacuum matrix elements of products of the interacting fields in such theories do not have delta function or principal value singularities in momentum space. We remedy this problem by constructing a field for the charged particle that does have the required singularities in momentum space. We illustrate this construction in quantum electrodynamics (QED).