Geometrical Properties and Propagation for the Proca Field Theory

TL;DR

This paper investigates the geometrical and propagation properties of the Proca field, demonstrating that the most general formulation with a dynamical exterior derivative is inconsistent, thus confirming the standard Proca theory as the most general form.

Contribution

The paper shows that extending the Proca field equations with a general connection leads to inconsistency, establishing the standard theory as the most general consistent formulation.

Findings

Generalized Proca equations are inconsistent with arbitrary connections.

The standard Proca theory is confirmed as the most general consistent formulation.

Propagation and geometrical properties are clarified within the standard framework.

Abstract

We consider the Proca field with dynamical term given by the exterior derivative with respect to the most general connection; the most general Proca field equations are given, and a discussion about the propagation and the geometrical properties are presented: it is shown that this generalization is inconsistent. So the standard theory is already the most general Proca Theory possible.