OPERATOR-FORMALISM ON THE Z(N) SYMMETRICAL ALGEBRAIC-CURVES

On Z(n) symmetric algebraic curves of any genus the Hilbert space of a nalytic free fields with integer spin is constructed. As an applicatio n, an operator formalism for the b-c systems is developed. The physica l states are expressed in terms bf creation and annihilation operators as in the complex plane and the correlation functions are evaluated e xploiting simple normal ordering rules. The formalism is very suitable for performing explicit calculations on Riemann surfaces and, moreove r, it gives some insight into the nature of two-dimensional field theo ries on a manifold. It is proven, in fact, that the b-c systems on a Z (n) symmetric algebraic curve sire equivalent to a conformal field the ory on the complex plane having as primary operators twist fields and free ghosts. Some consequences of the interplay between topology and s tatistics are also discussed. (C) 1995 American Institute of Physics.