Dressed Fermions, Modular Transformations and Bosonization in the Compactified Schwinger Model

TL;DR

This paper revisits the exactly solvable Schwinger model, highlighting the importance of topological sectors and large gauge transformations in its non-perturbative solution, especially under space compactification.

Contribution

It introduces a gauge-invariant quantization method that incorporates large gauge transformations and topological effects in the compactified Schwinger model.

Findings

Non-perturbative features are recovered in the massless case.

Fermion mass term affects gauge invariance and physical quantization.

Explicit gauge-invariant quantization avoids gauge fixing procedures.

Abstract

The celebrated exactly solvable "Schwinger" model, namely massless two-dimensional QED, is revisited. The solution presented here emphasizes the non- perturbative relevance of the topological sector through large gauge transformations whose role is made manifest by compactifying space into a circle. Eventually the well-known non-perturbative features and solution of the model are recovered in the massless case. However the fermion mass term is shown to play a subtle role in order to achieve a physical quantization that accounts for gauge invariance under both small and large gauge symmetries. Quantization of the system follows Dirac's approach in an explicitly gauge invariant way that avoids any gauge fixing procedure.