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arXiv · 1809.04601

Quantum effective action for degenerate vector field theories

Michael S. Ruf·Christian F. Steinwachs
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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.

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Michael S. Ruf, Christian F. Steinwachs. 2018-10-15. Quantum effective action for degenerate vector field theories. https://doi.org/10.1103/physrevd.98.085014

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