Remark on the computation of mode sums

TL;DR

This paper discusses methods for computing mode sums in quantum field theory, focusing on regularization and calculation of Casimir energies for various string models and their effects on interquark potentials.

Contribution

It introduces a regularization approach for mode sums and applies it to compute Casimir energies for different string configurations, including effects of external fields.

Findings

Casimir energy computed for continuum Nambu-Goto string with massive ends

Casimir energy calculated for discrete Isgur-Paton string with massive ends

Effect of Kalb-Ramond field on interquark potential analyzed

Abstract

The computation of mode sums of the types encountered in basic quantum field theoretic applications is addressed with an emphasis on their expansions into functions of distance that can be interpreted as potentials. We show how to regularize and calculate the Casimir energy for the continuum Nambu-Goto string with massive ends as well as for the discrete Isgur-Paton non-relativistic string with massive ends. As an additional example, we examine the effect on the interquark potential of a constant Kalb-Ramond field strength interacting with a QCD string.