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arXiv · 0708.0392

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

Ariel Edery·Ilana MacDonald
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Abstract

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 $a \to 1/a$ 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.

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Ariel Edery, Ilana MacDonald. 2007-08-29. Cancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston. https://doi.org/10.1088/1126-6708%2F2007%2F09%2F005

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