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arXiv · 1509.05989

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

David J. Toms
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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.

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David J. Toms. 2015-09-20. Quantization of the minimal and non-minimal vector field in curved space. https://arxiv.org/abs/1509.05989

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