Mechanical momentum in nonequilibrium quantum electrodynamics

TL;DR

This paper introduces a reformulation of quantum electrodynamics that focuses on mechanical momentum, providing a kinetic description that avoids divergences caused by unphysical canonical momentum, and offers a new way to connect distribution functions.

Contribution

It presents a novel approach to QED that replaces canonical momentum with mechanical momentum, eliminating divergences and enabling a kinetic description without approximations.

Findings

Divergences in QED are linked to unphysical canonical momentum.

A dressing operator connects distribution functions of canonical and mechanical momentum.

The reformulation allows a divergence-free kinetic description of electron dynamics.

Abstract

The reformulation of field theory in which self-energy processes are no longer present [Annals of Physics, {\bf311} (2004), 314.], [ Progr. Theor. Phys., {\bf 109} (2003), 881.], [Trends in Statistical Physics {\bf 3} (2000), 115.] provides an adequate tool to transform Swinger-Dyson equations into a kinetic description outside any approximation scheme. Usual approaches in quantum electrodynamics (QED) are unable to cope with the mechanical momentum of the electron and replace it by the canonical momentum. The use of that unphysical momentum is responsible for the divergences that are removed by the renormalization procedure in the $S$-matrix theory. The connection between distribution functions in terms of the canonical and those in terms of the mechanical momentum is now provided by a dressing operator [Annals of Physics, {\bf314} (2004), 10] that allows the elimination of the above divergences, as the first steps are illustrated here.