# Massive vector field on curved background: non-minimal coupling, quantization and divergences

## TL;DR

This paper investigates the quantum properties of a non-minimally coupled massive vector field in curved spacetime, deriving its divergences and analyzing its effective action with gauge invariance restored.

## Contribution

It provides a systematic analysis of the divergences and effective action structure for a non-minimally coupled massive vector field in curved backgrounds, using novel gauge fixing and variable transformations.

## Key findings

- Derived the complete divergence structure of the effective action.
- Developed a method to diagonalize the bilinear form of the action.
- Restored gauge invariance using Stueckelberg fields and special gauge fixing.

## Abstract

We study the effective action for the massive vector field theory non-minimally coupled to external gravitational field. Such a theory is an interesting model both from the theoretical side and also due to the various phenomenological applications to cosmology and astrophysics. The present work pretends to initiate a systematic study of its properties at the quantum level, by exploring free massive vector coupled to an external symmetric second-rank tensor. Stueckelberg scalar field is used to restore the gauge invariance. After that, by using a special gauge fixing and non-local in external fields change of variables, we diagonalize the bilinear form of the action and develop a consistent procedure to study the effective action. As a result we derive a complete non-linear structure of divergences of the effective action and discuss its properties.