Fields In Nonaffine Bundles II. Gauge coupled generalization of harmonic mappings and their Bunting identities

TL;DR

This paper extends harmonic mappings between Riemannian spaces to include gauge coupling, introducing a formalism that generalizes Bunting identities for establishing uniqueness in more complex geometric settings.

Contribution

It develops a gauge-coupled extension of harmonic mappings using a specialized gauge-covariant differentiation formalism, generalizing Bunting identities for broader geometric applications.

Findings

Generalized harmonic mappings to gauge-coupled cases

Extended Bunting identities to nonaffine bundles with gauge fields

Provided conditions for uniqueness in curved spaces

Abstract

The general purpose bitensorially gauge-covariant differentiation procedure set up in the preceding article is specialised to the particular case of bundles with nonlinear fibres that are endowed with a torsion free Riemannian or pseudo-Riemannian structure. This formalism is used to generalize the class of harmonic mappings between Riemannian or pseudo-Riemannian spaces to a natural gauge coupled extension in the form of a class of field sections of a bundle having the original image space as fibre, with a nonintegrable gauge connection $\Amr$ belonging to the algebra of the isometry group of the fibre space. The Bunting identity that can be used for establishing uniqueness in the strictly positive Riemannian case with negative image space curvature is shown to be generalizable to this gauge coupled extension.