The Schwinger Model and the Physical Projector: a Nonperturbative Quantization without Gauge Fixing

TL;DR

This paper presents a nonperturbative quantization of the massless Schwinger model using the physical projector approach, avoiding gauge fixing and clarifying the physical spectrum as a massive pseudoscalar field.

Contribution

It introduces a gauge-fixing-free quantization method for the Schwinger model, providing a clear physical spectrum without gauge artefacts.

Findings

The physical spectrum is a massive pseudoscalar field.

The approach avoids gauge fixing artefacts.

The spectrum differs from bound fermion-antifermion pairs.

Abstract

Based on the physical projector approach, a nonpertubative quantization of the massless Schwinger model is considered which does not require any gauge fixing. The spectrum of physical states, readily identified following a diagonalization of the operator algebra, is that of a massive pseudoscalar field, namely the electric field having acquired a mass proportional to the gauge coupling constant. The physical spectrum need not be identified with confined bound fermion-antifermion pairs, an interpretation which one is otherwise led to given whatever gauge fixing procedure but which is not void of gauge fixing artefacts.