Quantum Energy Density of Cosmic Strings with Nonzero Radius

TL;DR

This paper calculates quantum energy corrections around cosmic strings with finite radius using scattering theory, focusing on massless fields in 2+1 dimensions, and introduces precise renormalization methods.

Contribution

It develops a scattering theory approach for quantum corrections to cosmic string energy density with nonzero radius, employing novel renormalization and integral techniques.

Findings

Computed quantum energy density corrections for cosmic strings with finite radius.

Implemented unambiguous renormalization conditions in the presence of a deficit angle.

Utilized Kontorovich-Lebedev techniques to transform sums into integrals.

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.