A new look at the problem of gauge invariance in quantum field theory

TL;DR

This paper investigates the discrepancy between the assumed gauge invariance of quantum field theory and the non-gauge invariant results obtained through perturbation calculations, aiming to understand the underlying reasons.

Contribution

It provides an analysis of why quantum field theory yields non-gauge invariant results in perturbation theory despite gauge invariance being a fundamental assumption.

Findings

Identification of sources of non-gauge invariant terms in perturbation calculations

Clarification of the conditions under which gauge invariance is violated

Insights into how to properly handle gauge invariance in quantum field computations

Abstract

Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. In this paper we will examine this problem and determine why a theory that is supposed to be gauge invariant produces non-gauge invariant results.