2PI functional techniques for gauge theories: QED

TL;DR

This paper develops a renormalization framework for QED within 2PI functional techniques, ensuring gauge symmetry is preserved at all approximation levels, and provides practical methods for handling divergences.

Contribution

It introduces a systematic renormalization procedure for 2PI QED that maintains gauge invariance at any loop order, with detailed analysis of divergences and counterterms.

Findings

Renormalization of all n-point functions in 2PI QED achieved.

Gauge symmetry preserved through local counterterms.

Framework applicable at any approximation order.

Abstract

We discuss the formulation of the prototype gauge field theory, QED, in the context of two-particle-irreducible (2PI) functional techniques with particular emphasis on the issues of renormalization and gauge symmetry. We show how to renormalize all $n$-point vertex functions of the (gauge-fixed) theory at any approximation order in the 2PI loop-expansion by properly adjusting a finite set of local counterterms consistent with the underlying gauge symmetry. The paper is divided in three parts: a self-contained presentation of the main results and their possible implementation for practical applications; a detailed analysis of ultraviolet divergences and their removal; a number of appendices collecting technical details.