Bosonic Field Propagators on Algebraic Curves

Details Bosonic Field Propagators on Algebraic Curves Bosonic Field Propagators on Algebraic Curves

1999-09-23

arxiv.org/abs/hep-th/9909173v1

J.Math.Phys. 41 (2000) 6444-6462

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, TeX + harvmac

Scientific paper

10.1063/1.1286172

In this paper we investigate massless scalar field theory on non-degenerate algebraic curves. The propagator is written in terms of the parameters appearing in the polynomial defining the curve. This provides an alternative to the language of theta functions. The main result is a derivation of the third kind differential normalized in such a way that its periods around the homology cycles are purely imaginary. All the physical correlation functions of the scalar fields can be expressed in terms of this object. This paper contains a detailed analysis of the techniques necessary to study field theories on algebraic curves. A simple expression of the scalar field propagator is found in a particular case in which the algebraic curves have $Z_n$ internal symmetry and one of the fields is located at a branch point.

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