QED positronium and the exact renormalization group

TL;DR

This paper applies the exact renormalization group to quantum electrodynamics, incorporating bound state analysis of positronium via a scalar field and dimensional regularization, providing insights into long-distance QED phenomena.

Contribution

It introduces a novel ERG approach to QED that includes bound states like positronium through a scalar field and employs dimensional regularization for improved analysis.

Findings

Successful formulation of ERG equations with Ward identities

Description of positronium as a bound state within the ERG framework

Use of low-momentum expansion to analyze flow equations

Abstract

Quantum electrodynamics (QED) is studied in the framework of the exact (functional) renormalization group (ERG). This is done using an approach to these equations which employs dimensional regularization. Simultaneous solutions of the ERG equations and Ward identities are considered. An approach to the study of bound states at long distances in the ERG is employed to describe the positronium. This is done by introducing a real scalar field which describes that bound state. The flow equations are studied using an effective action ansatz and a low-momentum expansion.