Quantization of the minimal and non-minimal vector field in curved space

Abstract

The local momentum space method is used to study the quantized massive vector field (the Proca field) with the possible addition of non-minimal terms. Heat kernel coefficients are calculated and used to evaluate the divergent part of the one-loop effective action. It is shown that the naive expression for the effective action that one would write down based on the minimal coupling case needs modification. We adopt a Faddeev-Jackiw method of quantization and consider the case of an ultrastatic spacetime for simplicity. The operator that arises for non-minimal coupling to the curvature is shown to be non-minimal in the sense of Barvinsky and Vilkovisky. It is shown that when a general non-minimal term is added to the theory the result is not renormalizable with the addition of a local Lagrangian counterterm.

Cited by in corpus (4)

• Massive vector field on curved background: non-minimal coupling, quantization and divergences
• One-loop renormalization in Galileon effective field theory
• Renormalization of vector fields with mass-like coupling in curved spacetime
• Residual gauge-invariance in a massive Lorentz-violating extension of QED