Effective action for delta potentials: spacetime-dependent inhomogeneities and Casimir self-energy

• URL: http://arxiv.org/abs/2010.11144v2
• Date: Tue, 2 Mar 2021 14:11:36 GMT
• Title: Effective action for delta potentials: spacetime-dependent inhomogeneities and Casimir self-energy
• Authors: S. A. Franchino-Vi\~nas and F. D. Mazzitelli
• Abstract summary: We study the vacuum fluctuations of a quantum scalar field in the presence of a thin and inhomogeneous flat mirror, modeled with a delta potential. We show that the divergences can be absorbed into a local counterterm, and that the remaining finite part is in general a nonlocal functional of the inhomogeneities.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the vacuum fluctuations of a quantum scalar field in the presence of a thin and inhomogeneous flat mirror, modeled with a delta potential. Using Heat-Kernel techniques, we evaluate the Euclidean effective action perturbatively in the inhomogeneities (nonperturbatively in the constant background). We show that the divergences can be absorbed into a local counterterm, and that the remaining finite part is in general a nonlocal functional of the inhomogeneities, which we compute explicitly for massless fields in $D=4$ dimensions. For time-independent inhomogeneities, the effective action gives the Casimir self-energy for a partially transmitting mirror. For time-dependent inhomogeneities, the Wick-rotated effective action gives the probability of particle creation due to the dynamical Casimir effect.

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