Quantum Energy Density of Cosmic Strings with Nonzero Radius

Abstract

Zero-point fluctuations in the background of a cosmic string provide an opportunity to study the effects of topology in quantum field theory. We use a scattering theory approach to compute quantum corrections to the energy density of a cosmic string, using the "ballpoint pen" and "flowerpot" models to allow for a nonzero string radius. For computational efficiency, we consider a massless field in $2+1$ dimensions. We show how to implement precise and unambiguous renormalization conditions in the presence of a deficit angle, and make use of Kontorovich-Lebedev techniques to rewrite the sum over angular momentum channels as an integral on the imaginary axis.

12 pages, 9 .eps figures; v2: expanded discussion of sign and boundary behavior, added references and removed duplicate, slight improvements to numerics in figures, included covariant form of counterterm; v3: minor edits for style and notational consistency, version to be published in Phys Rev D; v4: fix minor typos; v5: correct figure file, fix typos; v6: correct grant number