Instantons and multi-instantons in curvilinear coordinates Original Research Article

Instantons in regular and singular gauges and explicit multi-instanton solutions are generalized to curvilinear coordinates. Expressions can be simplified by fitting gauge orientation of the solutions to the vierbein. The gauge transformation replaces η -symbols used in Cartesian formalism by constant ξ -symbols and generates a compensating addition to the gauge potential of pseudoparticles. Typical examples (4-spherical, (2+2) - and (3+1) -cylindrical coordinates) are studied explicitly. Effects of singularities of the compensating field on gauge dependent quantities are discussed.