Quantum effective action for degenerate vector field theories

Abstract

We calculate the divergent part of the one-loop effective action in curved spacetime for a particular class of second-order vector field operators with a degenerate principal part. The principal symbol of these operators has the structure of a longitudinal projector. In this case, standard heat-kernel techniques are not directly applicable. We present a method which reduces the problem to a nondegenerate scalar operator for which standard heat-kernel techniques are available. Interestingly, this method leads to the identification of an effective metric structure in the longitudinal sector. The one-loop divergences are compactly expressed in terms of invariants constructed from this metric.

arXiv comment6 pages, no figures; typos corrected, references added, accepted for publication in Phys. Rev. D

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• On constrained analysis and diffeomorphism invariance of generalised Proca theories
• Scattering approach for calculating one-loop effective action and vacuum energy