A Special Basis of the Space of Meromorphic Sections on Riemann Surfaces

Abstract

A special choice of basis for meromorphic sections of line bundles, in which all poles lie at the punctures, allows the decomposition of field operators (which are sections of bundles) into modes analogous to the standard decomposition on the sphere. Many of the calculational techniques used on the sphere can be reproduced for higher genus surfaces in this basis. Using this technique, in this paper, we compute a basis of Kγ (the space of meromorphic sections on a Riemann surface, holomorphic away from two fixed points). This basis consists of the sections which have the expected zero or pole order at the two points.