Operator Formalism on General Algebraic Curves

Details Operator Formalism on General Algebraic Curves Operator Formalism on General Algebraic Curves

1994-09-21

arxiv.org/abs/hep-th/9409127v2

Physics

High Energy Physics

High Energy Physics - Theory

34 pages of plain TeX + harvmac, With respect to the first version some new references have been added and a statement in the

Scientific paper

The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems is developed. The physical states are expressed by means of creation and annihilation operators as in the complex plane and the correlation functions are evaluated starting from simple normal ordering rules. The Hilbert space of the theory exhibits an interesting internal structure, being splitted into $n$ ($n$ is the number of branches of the curve) independent Hilbert spaces. Exploiting the operator formalism a large collection of explicit formulas of string theory is derived.

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