Justification of the zeta function renormalization in rigid string model

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. PACS numbers: 11.10.Gh, 11.00.Kk, 11.10.Wx ∗Permanent address: Petrozavodsk State University, Petrozavodsk, 185640, Russia