Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
