Justification of the zeta function renormalization in rigid string model

TL;DR

This paper justifies the use of zeta function regularization in the rigid string model, providing a consistent method for divergence treatment and deriving a spectral representation for the renormalized string energy.

Contribution

It offers a rigorous justification for zeta function regularization in the rigid string model and derives a spectral representation for the renormalized energy.

Findings

Justification of zeta function regularization for divergences.

Spectral representation for renormalized string energy.

Simplified calculation of Casimir energy at nonzero temperature.

Abstract

A consistent procedure for regularization of divergences and for the subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov-Kleinert string. In this way, a justification of the formal treatment of divergences by analytic continuation of the Riemann and Epstein-Hurwitz zeta functions is given. A spectral representation for the renormalized string energy at zero temperature is derived, which enables one to find the Casimir energy in this string model at nonzero temperature very easy.