The Schwinger model on the Torus

TL;DR

This paper analyzes the Schwinger model on a torus, explicitly finding zero modes, deriving the effective action, and calculating correlation functions, confirming known results in the infinite volume limit.

Contribution

It provides an explicit analysis of zero modes, effective action, and correlation functions for the Schwinger model on a torus, extending understanding of its quantum properties.

Findings

Explicit zero modes in topological sectors identified

Effective action and propagators derived

Chiral condensate and clustering properties confirmed

Abstract

The classical and quantum aspects of the Schwinger model on the torus are considered. First we find explicitly all zero modes of the Dirac operator in the topological sectors with nontrivial Chern index and is spectrum. In the second part we determine the regularized effective action and discuss the propagators related to it. Finally we calculate the gauge invariant averages of the fermion bilinears and correlation functions of currents and densities. We show that in the infinite volume limit the well-known result for the chiral condensate can be obtained and the clustering property can be established.