Bosonization, τ-functions and operator formalism on Riemann surfaces

We propose an operator bosonization of generalized ghost systems of closed string theory (the bc-system of spin J) on Riemann surfaces of arbitrary genus. The bosonization is carried out at the operator level in terms of Bose conformal field theory operators which are well-defined globally on the Riemann surface and are essentially given by operator-valued Baker-Akhiezer functions. The formalism yields an elementary derivation of higher-loop bc-correlation functions as well as a bosonic operator realization of the algebro-geometric tau function of arbitrary Riemann surfaces. It also enables us to construct explicitly an operator that glues a handle to Riemann surfaces. (orig.)