Operator bosonization on Riemann surfaces: new vertex operators

A new formalism is presented for building an operator theory of generalized ghost systems (bc theories of spin J) on Riemann surfaces (loop diagrams of the closed string theory). Operators of the bc system are expressed through the operators of a bosonic conformal theory on a Riemann surface. As distinct from standard bosonization formulas, which have meaning only locally, the Baker-Akhiezer operator functions are introduced which are globally well defined on a Riemann surface of arbitrary form. The operator algebra of Baker-Akhiezer functions generates explicity the algebraic-geometrical τ function and correlation functions of bc systems on Riemann surfaces