Vacuum Polarization Energy of a Nonzero Radius Cosmic String

Abstract

We calculate the vacuum polarization energy (VPE) of a scalar field in the background of a nonsingular cosmic string in $2+1$ spacetime dimensions. Our calculation expresses the VPE as a renormalized sum and integral over scattering data, which can be expressed in terms of Legendre and Bessel functions for the "ballpoint pen" model, analogous to a square well in curvature, and which can be obtained numerically for a generic string profile. We show how relationships between the local density of states, expressed in terms of the Green's function, and the global density of states, expressed in terms of the Jost function, extend to this curved spacetime background and allow for precise implementation of perturbative renormalization conditions.