1998/11/20 by Marco Scandurra · 4 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Quantum Electrodynamics and Casimir Effect #Quantum, superfluid, helium dynamics #hep-th
paper · pdf · doi:10.1088/0305-4470/32/30/312
published as J.Phys.A32:5679-5691,1999 · 15 pages, 5 figures
arxiv created 1998/11/20 · openalex publication_date 1999/07/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We calculate the zero-point energy of a massive scalar field in the background of an infinitely thin spherical shell given by a potential of the delta-function type. We use zeta-functional regularization and express the regularized ground state energy (GSE) in terms of the Jost function of the related scattering problem. We then find the corresponding heat-kernel coefficients and perform the renormalization, imposing the normalization condition that the GSE vanishes when the mass of the quantum field becomes large. Finally, the GSE is calculated numerically. Corresponding plots are given for different values of the strength of the background potential, for both attractive and repulsive potentials. The formal transition from a delta-function potential to Dirichlet boundary conditions is not found to take place in the renormalized GSE.