Flow equations for QED in the light front dynamics

TL;DR

This paper applies flow equations to QED in light front dynamics, simplifying the positronium problem by eliminating particle number violating terms and avoiding infrared divergences, while enabling simultaneous ultraviolet renormalization.

Contribution

It introduces a novel application of flow equations to QED on the light front, effectively reducing the positronium problem to a two-particle system with renormalization.

Findings

Elimination of infrared divergences

Reduction of positronium to a two-particle problem

Simultaneous ultraviolet renormalization

Abstract

The method of flow equations is applied to QED on the light front. Requiring that the partical number conserving terms in the Hamiltonian are considered to be diagonal and the other terms off-diagonal an effective Hamiltonian is obtained which reduces the positronium problem to a two-particle problem, since the particle number violating contributions are eliminated. No infrared divergencies appear. The ultraviolet renormalization can be performed simultaneously.