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arXiv · 2010.11144

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

S. A. Franchino-Viñas·F. D. Mazzitelli
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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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S. A. Franchino-Viñas, F. D. Mazzitelli. 2020-10-21. Effective action for delta potentials: spacetime-dependent inhomogeneities and Casimir self-energy. https://doi.org/10.1103/physrevd.103.065006

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