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.
Keywords
Cite
@article{arxiv.1509.05989,
title = {Quantization of the minimal and non-minimal vector field in curved space},
author = {David J. Toms},
journal= {arXiv preprint arXiv:1509.05989},
year = {2015}
}