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arXiv · hep-th/9406048

Casimir effect for a $D$-dimensional sphere

Carl M. Bender·Kimball A. Milton
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Abstract

The Casimir force on a $D$-dimensional sphere due to the confinement of a massless scalar field is computed as a function of $D$, where $D$ is a continuous variable that ranges from $-\infty$ to $\infty$. The dependence of the force on the dimension is obtained using a simple and straightforward Green's function technique. We find that the Casimir force vanishes as $D\to +\infty$ ($D$ non-even integer) and also vanishes when $D$ is a negative even integer. The force has simple poles at positive even integer values of $D$.

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Carl M. Bender, Kimball A. Milton. 1994-06-08. Casimir effect for a $D$-dimensional sphere. https://doi.org/10.1103/physrevd.50.6547

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