Casimir self-energy of a δ-δ' sphere

Abstract

We extend previous work on the vacuum energy of a massless scalar field in the presence of singular potentials. We consider a single sphere denoted by the so-called "delta-delta prime" interaction. Contrary to the Dirac delta potential, we find a nontrivial one-parameter family of potentials such that the regularization procedure gives an unambiguous result for the Casimir self-energy. The procedure employed is based on the zeta function regularization and the cancellation of the heat kernel coefficient a_2. The results obtained are in agreement with particular cases, such as the Dirac delta or Robin and Dirichlet boundary conditions.

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Cited by in corpus (3)

• Casimir energy for spinor fields with $\delta$-shell potentials
• Generalized Neumann boundary condition for the scalar field
• Vacuum energy of scalar fields on spherical shells with general matching conditions