Generalized Proca action for an Abelian vector field

TL;DR

This paper develops a comprehensive theoretical framework for a massive vector field with derivative self-interactions, extending previous models to include trivial total derivatives and curvature effects, providing a basis for further studies in modified gravity.

Contribution

It introduces the most general form of the generalized Proca action, including trivial total derivative interactions and curvature terms, for a massive vector field.

Findings

All possible terms with up to five derivatives in flat spacetime identified

Conjecture proposed for higher-order derivative terms

Covariantized action includes all curvature-related interactions

Abstract

We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the flat spacetime (Minkowski) case, we obtain all the possible terms containing products of up to five first-order derivatives of the vector field, and provide a conjecture about higher-order terms. Rendering the metric dynamical, we covariantize the results and add all possible terms implying curvature.