Casimir energy for self-interacting scalar field in a spherical shell

TL;DR

This paper calculates the Casimir energy for a massless self-interacting scalar field in a spherical shell, addressing divergences and applying renormalization to obtain finite results.

Contribution

It introduces a method to compute Casimir energy with self-interacting fields using zeta function regularization and renormalization techniques.

Findings

Divergent contributions are identified and canceled through renormalization.

Self-interacting terms mimic the effect of mass in the Casimir energy.

Finite Casimir energy results are obtained after renormalization.

Abstract

In this paper we calculate the Casimir energy for spherical shell with massless self-interacting scalar filed which satisfying Dirichlet boundary conditions on the shell. Using zeta function regularization and heat kernel coefficients we obtain the divergent contributions inside and outside of Casimir energy. The effect of self-interacting term is similar with existing of mass for filed. In this case some divergent part arises. Using the renormalization procedure of bag model we can cancel these divergent parts.