A ug 2 00 7 Cancellation of nonrenormalizable hypersurface divergences and the d - dimensional
نویسنده
چکیده
Using 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 → 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:0705.0139v1 [quant-ph] using an optical path technique providing an independent confirmation of our multidimensional approach. We limit our study to massless scalar fields. ∗Email: [email protected]
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