2020/10/31 by S. A. Franchino-Viñas, F. D. Mazzitelli, Francisco D. Mazzitelli
Mathematics · Physics and Astronomy · #Action (physics) #Casimir effect #Classical mechanics #Cosmology and Gravitation Theories #Effective action #Euclidean geometry #Geometry #Massless particle #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum electrodynamics #Quantum fluctuation #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Scalar field #Scalar field theory #Spacetime #Vacuum energy #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.103.065006
published as Phys. Rev. D 103, 065006 (2021) · 25 pages, 4 figures. Added a discussion on the renormalization process. Added some missing factors in formulas (72) and (73), App. A
arxiv created 2021/03/02 · openalex publication_date 2021/03/16 · arxiv updated 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.