Quantum Field Theories on Algebraic Curves

TL;DR

This paper reviews the operator formalism for $b-c$ systems on algebraic curves, introducing algebraic curve techniques and presenting new results on operator algebra representations and divisor calculations.

Contribution

It develops a detailed operator formalism for $b-c$ systems on algebraic curves and introduces new methods for representing operator algebras and calculating divisors.

Findings

New representation of $b-c$ operator algebra

Explicit techniques for constructing meromorphic tensors

Results on divisor calculations on algebraic curves

Abstract

In this talk the main features of the operator formalism for the $b-c$ systems on general algebraic curves developed in refs. [1-2] are reviewed. The first part of the talk is an introduction to the language of algebraic curves. Some explicit techniques for the construction of meromorphic tensors are explained. The second part is dedicated to the discussion of the $b-c$ systems. Some new results concerning the concrete representation of the basic operator algebra of the $b-c$ systems and the calculation of divisors on algebraic curves have also been included.