  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.
