The Casimir effect as scattering problem

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dc.creatorWirzba, Andreas
dc.date2007-11-15
dc.date2008-02-11
dc.date.accessioned2026-07-07T11:13:12Z
dc.date.available2026-07-07T11:13:12Z
dc.descriptionWe show that Casimir-force calculations for a finite number of non-overlapping obstacles can be mapped onto quantum-mechanical billiard-type problems which are characterized by the scattering of a fictitious point particle off the very same obstacles. With the help of a modified Krein trace formula the genuine/finite part of the Casimir energy is determined as the energy-weighted integral over the log-determinant of the multi-scattering matrix of the analog billiard problem. The formalism is self-regulating and inherently shows that the Casimir energy is governed by the infrared end of the multi-scattering phase shifts or spectrum of the fluctuating field. The calculation is exact and in principle applicable for any separation(s) between the obstacles. In practice, it is more suited for large- to medium-range separations. We report especially about the Casimir energy of a fluctuating massless scalar field between two spheres or a sphere and a plate under Dirichlet and Neumann boundary conditions. But the formalism can easily be extended to any number of spheres and/or planes in three or arbitrary dimensions, with a variety of boundary conditions or non-overlapping potentials/non-ideal reflectors.
dc.description14 pages, 2 figures, plenary talk at QFEXT07, Leipzig, September 2007, some typos corrected
dc.identifierhttps://arxiv.org/abs/0711.2395
dc.identifierhttp://arxiv.org/abs/0711.2395
dc.identifierJ.Phys.A41:164003,2008
dc.identifierdoi:10.1088/1751-8113/41/16/164003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/191638
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectChaotic Dynamics
dc.subjectNuclear Theory
dc.titleThe Casimir effect as scattering problem
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