Casimir energies in spherically symmetric background potentials revisited

Abstract

In this paper we reconsider the formulation for the computation of the Casimir energy in spherically symmetric background potentials. Compared to the previous analysis, the technicalities are much easier to handle and final answers are surprisingly simple.

arXiv comment14 pages, 6 figures

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• Casimir Energy for concentric $\delta$-${\delta }^{\prime }$ spheres
• Hyperspherical $\delta \text{-}{\delta }^{\prime }$ potentials
• Vacuum polarization with zero-range potentials on a hyperplane
• Functional determinants and Casimir energy in higher dimensional spherically symmetric background potentials
• Probability Thermodynamics and Probability Quantum Field
• Casimir effect for scalar field rotating on a disk
• Scattering approach for calculating one-loop effective action and vacuum energy