A topological state sum model for fermions on the circle

TL;DR

This paper introduces a triangulation-independent state sum model for fermions on a circle that matches the Dirac functional integral's partition function, with potential implications for physical models.

Contribution

It presents a novel topological state sum model for fermions on a 1-manifold that reproduces known quantum field theory results.

Findings

Model is triangulation-independent

Partition function matches Dirac functional integral with zeta regularization

Implications discussed for more realistic physical models

Abstract

A simple state sum model for fermions on a 1-manifold is constructed. The model is independent of the triangulation and gives exactly the same partition function as the Dirac functional integral with zeta-function regularisation. Some implications for more realistic physical models are discussed.