Dressed fermions, modular transformations and bosonization in the compactified Schwinger model

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.