The topological quantum field theory of Riemann's theta functions

TL;DR

This paper establishes a unique topological quantum field theory that models Riemann's theta functions and their symmetries across all Riemann surfaces, linking complex analysis and quantum topology.

Contribution

It proves the existence and uniqueness of a TQFT that encodes theta functions and their symmetry groups for all Riemann surfaces, a novel integration of these mathematical structures.

Findings

Existence of a TQFT incorporating Riemann's theta functions.

Uniqueness of this TQFT for all Riemann surfaces.

Modeling of Heisenberg and modular group actions within the TQFT.

Abstract

In this paper we prove the existence and uniqueness of a topological quantum field theory that incorporates, for all Riemann surfaces, the corresponding spaces of theta functions and the actions of the Heisenberg groups and modular groups on them.