Operator Formalism on General Algebraic Curves

Abstract

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.

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

References in corpus (5)

• Form Factors, deformed Knizhnik-Zamolodchikov equations and finite-gap integration
• Multivalued Fields on the Complex Plane and Conformal Field Theories
• Operator Formalism on the $Z_n$ Symmetric Algebraic Curves
• Multivalued Fields on the Complex Plane and Braid Group Statistics
• Relation Between Hyperelliptic Integrals

Cited by in corpus (5)

• Operator Formalism on the $Z_n$ Symmetric Algebraic Curves
• Bosonic Field Propagators on Algebraic Curves
• Operator Formalism for Bosonic Beta-Gamma Fields on General Algebraic Curves
• Topologically Nontrivial Sectors of the Maxwell Field Theory on Algebraic Curves
• Monodromy Properties of the Energy Momentum Tensor on General Algebraic Curves