Casimir self-energy of a \delta-\delta' sphere

TL;DR

This paper calculates the Casimir self-energy for a scalar field interacting with a sphere modeled by a delta-delta prime potential, revealing a well-defined regularization method and consistent results with known boundary conditions.

Contribution

It introduces a new regularization approach for the Casimir energy of a delta-delta prime sphere, extending previous models and resolving ambiguities in the self-energy calculation.

Findings

A one-parameter family of potentials yields unambiguous Casimir energies.

The regularization method based on zeta function and heat kernel cancellation is effective.

Results agree with known cases like Dirac delta and Robin boundary conditions.

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.