Topological Charge in Curved Spacetime

TL;DR

This paper extends the concept of topological gauge field theory from flat to curved spacetime by developing a new derivation of topological charge that incorporates scalar curvature, enabling analysis in curved backgrounds.

Contribution

It introduces a novel derivation of topological charge applicable to curved spacetime, overcoming limitations of previous instanton-based methods.

Findings

Derived a new expression for topological charge in curved spacetime.

Coupled relativistic quantum mechanics equations with scalar curvature.

Enabled quantization analysis of topological charge in curved backgrounds.

Abstract

This paper presents the extension from flat spacetime into curved spacetime of the area of theoretical investigation that has been known as topological gauge field theory. The extension here presented is based upon a new derivation of the expression for topological charge for bosons and fermions in flat spacetime, a derivation which has been presented elsewhere [1]. This new approach was developed because the established instanton solution could not be extended to curved spacetime. The new approach can be extended to curved spacetime by coupling the major equations of relativistic quantum mechanics to the scalar curvature. The coupling here presented, and results obtained about the quantization of topological charge, had not been possible with the earlier established instanton solution.