Instantons in curvilinear coordinates
Alexei A. Abrikosov Jr
TL;DR
This paper generalizes multi-instanton solutions to curvilinear coordinates, simplifying expressions via gauge transformations and analyzing the role of singularities in gauge-dependent quantities.
Contribution
It introduces a method to extend instanton solutions to curvilinear coordinates and clarifies the impact of singularities on gauge-dependent aspects.
Findings
Simplified instanton expressions in curvilinear coordinates
Gauge transformations generate compensating gauge potentials
Singularities do not affect physical observables
Abstract
The multi-instanton solutions by 'tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. Expressions can be notably simplified by the appropriate gauge transformation. This generates the compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating connection are irrelevant for physics but affect gauge dependent quantities.
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