Massive vector field on curved background: Nonminimal coupling, quantization, and divergences
We study the effective action for the massive vector field theory nonminimally 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 nonlocal 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 nonlinear structure of divergences of the effective action and discuss its properties.