Vacuum polarization and the geometric phase: Gauge invariance

TL;DR

This paper presents a nonperturbative method to analyze vacuum polarization in quantum field theory, demonstrating gauge and renormalization invariance of the geometric phase through appropriate counterterms.

Contribution

It introduces a gauge-invariant, nonperturbative approach to vacuum polarization and clarifies the role of counterterms in maintaining invariance of the geometric phase.

Findings

Vacuum polarization phase is gauge invariant

Vacuum polarization phase is renormalization independent

Counterterms can be chosen to ensure invariance

Abstract

A nonperturbative approach to the vacuum polarization for quantized fermions in external vector potentials is discussed. It is shown that by a suitable choice of counterterms the vacuum polarization phase is both gauge and renormalization independent, within a large class of nonperturbative renormalizations.