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

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.

19 pages. A few references added. Accepted in PRD

References in corpus (8)

• Vector Inflation
• Cosmology of the proxy theory to massive gravity
• Generalized Galileon Duality
• Non-minimally coupled vector curvaton
• Generalized multi-Proca fields
• Quantum Effects in Softly Broken Gauge Theories in Curved Space-Times
• Quantum corrections to the generalized Proca theory via a matter field
• Vacuum contribution of photons in the theory with Lorentz and CPT-violating terms

Cited by in corpus (13)

• Spontaneous Lorentz symmetry breaking and one-loop effective action in the metric-affine bumblebee gravity
• Renormalization of generalized vector field models in curved spacetime
• Runaway Gravitational Production of Dark Photons
• One-loop renormalization in Galileon effective field theory
• Geometrized quantum Galileons
• One-loop renormalization of Lorentz/CPT violating scalar field theory in curved space-time
• Gravitational Properties of the Proca Field
• Unveiling the inconsistency of the Proca theory with non-minimal coupling to gravity
• Heat kernel coefficients for massive gravity
• Renormalization of vector fields with mass-like coupling in curved spacetime
• Consistency of an alternative CPT-odd and Lorentz-violating extension of QED
• Residual gauge-invariance in a massive Lorentz-violating extension of QED
• Non-minimal non-Abelian quantum vector fields in curved spacetime