Wave Equations for Classical Two-Component Proca Fields in Curved Spacetimes with Torsionless Affinities

TL;DR

This paper reviews the classical Proca field theory in curved spacetimes, deriving wave equations that describe their propagation, and finds that these fields do not couple directly to electromagnetic curvature but interact with gravitons.

Contribution

It provides a concise formulation of Proca fields in curved spacetimes using Infeld-van der Waerden formalism and derives wave equations highlighting their interaction structure.

Findings

Wave equations for Proca fields are derived in curved spacetimes.

Proca fields do not couple directly to electromagnetic curvatures.

Interactions are limited to Proca fields and gravitons.

Abstract

The world formulation of the full theory of classical Proca fields in generally relativistic spacetimes is concisely reviewed and the entire set of pertinent field equations is transcribed in a straightforward way into the framework of one of the Infeld-van der Waerden formalisms. Some well-known calculational techniques are then utilized for deriving the wave equations that control the propagation of the fields allowed for. It appears that no interaction couplings between such fields and electromagnetic curvatures are carried by the wave equations at issue. What results is, in effect, that the only interactions which ultimately occur in the theoretical context under consideration involve strictly Proca fields and wave functions for gravitons.