The Atiyah-Singer fixed point theorem and the gauge field copy problem

TL;DR

This paper presents a condition involving the Lefschetz number that determines when false gauge field copies can exist, linking topological invariants to gauge theory issues.

Contribution

It introduces a novel criterion based on the Lefschetz number for identifying false gauge field copies in gauge theories.

Findings

Derived a condition using Lefschetz number for gauge copy existence

Connected topological invariants with gauge field configurations

Provided insights into the gauge copy problem

Abstract

A condition for the existence of false gauge field copies in terms of the Lefschetz number of a certain differential operator is presented.