Instantons in non-Cartesian coordinates

TL;DR

This paper generalizes multi-instanton solutions to curvilinear coordinates using gauge transformations, which simplify the expressions and introduce compensating fields affecting gauge-dependent quantities but not physical observables.

Contribution

It extends explicit multi-instanton solutions to non-Cartesian coordinates by employing gauge transformations to manage resulting complexities.

Findings

Gauge transformations simplify instanton expressions in curvilinear coordinates.

Compensating gauge fields arise from coordinate changes but do not affect physical results.

Singularities in compensating fields are gauge-dependent and physically irrelevant.

Abstract

The explicit multi-instanton solutions by 'tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. The idea is that a gauge transformation can notably simplify the expressions obtained after the change of variables. The gauge transform generates a compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating field are irrelevant for physics but may affect gauge dependent quantities.