Cancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston

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dc.creatorEdery, Ariel
dc.creatorMacDonald, Ilana
dc.date2007-08-02
dc.date2007-08-29
dc.date.accessioned2026-07-07T12:59:15Z
dc.date.available2026-07-07T12:59:15Z
dc.descriptionUsing a multidimensional cut-off technique, we obtain expressions for the cut-off dependent part of the vacuum energy for parallelepiped geometries in any spatial dimension d. The cut-off part yields nonrenormalizable hypersurface divergences and we show explicitly that they cancel in the Casimir piston scenario in all dimensions. We obtain two different expressions for the d-dimensional Casimir force on the piston where one expression is more convenient to use when the plate separation a is large and the other when a is small (a useful $a \to 1/a$ duality). The Casimir force on the piston is found to be attractive (negative) for any dimension d. We apply the d-dimensional formulas (both expressions) to the two and three-dimensional Casimir piston with Neumann boundary conditions. The 3D Neumann results are in numerical agreement with those recently derived in arXiv:0705.0139 using an optical path technique providing an independent confirmation of our multidimensional approach. We limit our study to massless scalar fields.
dc.description29 pages; 3 figures; references added; to appear in JHEP
dc.identifierhttps://arxiv.org/abs/0708.0392
dc.identifierhttp://arxiv.org/abs/0708.0392
dc.identifierJHEP 0709:005,2007
dc.identifierdoi:10.1088/1126-6708/2007/09/005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225515
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleCancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston
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