Effective action for delta potentials: spacetime-dependent inhomogeneities and Casimir self-energy
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 backgr...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
16 March 2021
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| In: |
Physical review
Year: 2021, Volume: 103, Issue: 6, Pages: 1-17 |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/PhysRevD.103.065006 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1103/PhysRevD.103.065006 Verlag, lizenzpflichtig, Volltext: https://link.aps.org/doi/10.1103/PhysRevD.103.065006 
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| Author Notes: | S.A. Franchino-Viñas and F.D. Mazzitelli |
| 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. 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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| Physical Description: | Online Resource |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/PhysRevD.103.065006 |