Casimir effect for a $D$-dimensional sphere

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 $D$.

22 pages, REVTeX, 4 uuencoded figures, OKHEP-94-05

References in corpus (4)

• Dimensional Expansion for the Ising Limit of Quantum Field Theory
• Determination of $\mathbf{f}(\infty )$ from the Asymptotic Series for $\mathbf{f}(\mathbf{x})$ About $\mathbf{x}=0$
• Random Walks in Noninteger Dimension
• Spherically-Symmetric Random Walks in Noninteger Dimension

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