Vacuum energy of scalar fields on spherical shells with general matching conditions

Abstract

In this work we analyze the spectral zeta function for massless scalar fields propagating in a $D$-dimensional flat space under
the influence of a shell potential. The static nature of the potential, and the spherical symmetry, allows us to focus on the spatial part of the field which satisfies a one-dimensional Schrodinger equation endowed with a point potential. 
The shell potential is defined in terms of the two-interval self-adjoint extensions of the one-dimensional Schrodinger equation that describes the radial part of the scalar field. After performing the necessary analytic continuation, we utilize the spectral zeta function 
of the system to compute the vacuum energy of the field.