Multiinstantons in curvilinear coordinates

TL;DR

This paper generalizes 'tHooft's multiinstanton solutions to curvilinear coordinates, simplifying expressions via gauge transformations and analyzing the properties and singularities of the resulting fields.

Contribution

It introduces a method to extend multiinstanton solutions to various curvilinear coordinate systems using gauge transformations and vierbein formalism.

Findings

Explicit formulas for multiinstantons in spherical and cylindrical coordinates.

Simplification of solutions through gauge transformations with constant eta-symbols.

Discussion of singularities and their physical relevance.

Abstract

The 'tHooft's 5N-parametric multiinstanton solution is generalized to curvilinear coordinates. Expressions can be simplified by a gauge transformation that makes $\eta$-symbols constant in the vierbein formalism. This generates the compensating addition to the gauge potential of pseudoparticles. Typical examples (4-spherical, 2+2- and 3+1-cylindrical coordinates) are studied and explicit formulae presented for reference. Singularities of the compensating field are discussed. They are irrelevant for physics but affect gauge dependent quantities.