Quantum energy density of cosmic strings with nonzero radius

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:math> 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. Published by the American Physical Society 2024