Path integral regularization of QED by means of Stueckelberg fields

TL;DR

This paper introduces a gauge-invariant regularization method for QED using Stueckelberg fields, resulting in a convergent action that reproduces QED predictions at tree and one-loop levels.

Contribution

It presents a novel regularization scheme for QED employing Stueckelberg fields to maintain gauge invariance and ensure convergence of the theory.

Findings

Regularized gauge-invariant QED action constructed.

The regularized action converges to standard QED as cutoff increases.

Reproduces QED predictions at tree and one-loop levels.

Abstract

With the help of a Stueckelberg field we construct a regularized U(1) gauge invariant action through the introduction of cutoff functions. This action has the property that it converges formally to the unregularized action of QED when the ultraviolet cutoff goes to infinity. Integrating out exactly the Stueckelberg field we obtain a simple effective regularized action, which is fully gauge invariant and gives rise to the same prediction as QED at the tree level and to the one loop order.