Fermionic Determinant of the Massive Schwinger Model

TL;DR

This paper derives a new representation for the fermionic determinant in the massive Schwinger model, clarifying its relation to gauge invariance, the index theorem, and field strength effects.

Contribution

It introduces a representation that separates the massless and massive contributions to the fermionic determinant in $QED_2$, linking gauge invariance to the index theorem.

Findings

The index theorem for $QED_2$ follows from gauge invariance.

The Schwinger model's contribution cancels in the weak field limit.

The determinant vanishes when the field forms a zero-energy bound state.

Abstract

A representation for the fermionic determinant of the massive Schwinger model, or $QED_2$, is obtained that makes a clean separation between the Schwinger model and its massive counterpart. From this it is shown that the index theorem for $QED_2$ follows from gauge invariance, that the Schwinger model's contribution to the determinant is canceled in the weak field limit, and that the determinant vanishes when the field strength is sufficiently strong to form a zero-energy bound state.