NONSTANDARD CONFORMAL FIELD-THEORIES FROM THE B-C SYSTEMS ON GENERAL ALGEBRAIC-CURVES

In this paper we develop an operator formalism for the b-c systems wit h conformal weight lambda = 1 defined on a general closed and orientab le Riemann surface. The advantage of our approach is that the Riemann surface is represented as an affine algebraic curve. In his way it is possible to show that the b-c systems at higher genera are equivalent to nonstandard conformal field theories on the complex sphere. The amp litudes of these conformal field theories, rigorously computed using s imple normal ordering prescriptions, are single-valued on the algebrai c curve and coincide with the correlation functions of the original b- c systems. Besides the obvious applications in string theories and con formal field theories, (the b-c systems at lambda = 1 are intimately r elated to the free scalar field theory), the operator formalism presen ted here also sheds some light on the quantization of field theories o n Riemann surfaces.