Zeta-function approach to Casimir energy with singular potentials

TL;DR

This paper uses the zeta-function approach to analyze Casimir energy in systems with singular potentials, proposing a renormalization method that yields physically consistent, finite energies and explores surface effects and effective action contributions.

Contribution

It introduces a renormalization scheme for Casimir energy with singular potentials using zeta-function subtraction, ensuring physically meaningful results.

Findings

Energy is finite after renormalization and obeys physical conditions.

Casimir energy can be attractive or repulsive depending on potential strength.

Surface contributions appear in the effective action.

Abstract

In the framework of zeta-function approach the Casimir energy for three simple model system: single delta potential, step function potential and three delta potentials is analyzed. It is shown that the energy contains contributions which are peculiar to the potentials. It is suggested to renormalize the energy using the condition that the energy of infinitely separated potentials is zero which corresponds to subtraction all terms of asymptotic expansion of zeta-function. The energy obtained in this way obeys all physically reasonable conditions. It is finite in the Dirichlet limit and it may be attractive or repulsive depending on the strength of potential. The effective action is calculated and it is shown that the surface contribution appears. The renormalization of the effective action is discussed.