Gauge Invariance in Nonlocal Regularized QED

TL;DR

This paper proves the existence of a gauge-invariant measure in nonlocal regularized QED, ensuring gauge invariance and unitarity at all orders, and discusses limitations in anomalous theories.

Contribution

It demonstrates the all-orders existence of the invariant measure in nonlocal regularized QED and analyzes its breakdown in anomalous theories.

Findings

Invariant measure exists to all orders in nonlocal regularized QED.

The measure maintains gauge invariance and perturbative unitarity.

Breakdown occurs in anomalous theories.

Abstract

The existence of the invariant measure in nonlocal regularized actions is discussed. It is shown that the measure for nonlocally regularized QED, as presented in\cite{Moff-Wood}, exists to all orders, and is precisely what is required to maintain gauge invariance at one loop and guarantees perturbative unitarity. We also demonstrate how the given procedure breaks down in anomalous theories, and discuss its generalization to other actions.