Light-Cone Quantization of the Schwinger Model

TL;DR

This paper develops a canonical quantum formulation of the Schwinger model using light-cone quantization, revealing a consistent operator solution with residual gauge freedoms and a nontrivial vacuum structure.

Contribution

It introduces a novel light-cone quantization approach for the Schwinger model, including a consistent operator solution and analysis of residual gauge degrees of freedom.

Findings

Constructed a consistent quantum theory in light-cone gauge

Derived quantization conditions compatible with field equations

Revealed a nontrivial vacuum structure with residual gauge freedoms

Abstract

We consider constructing a canonical quantum theory of the light-cone gauge ($A_-$=0) Schwinger model in the light-cone representation. Quantization conditions are obtained by requiring that translational generators $P_+$ and $P_-$ give rise to Heisenberg equations which, in a physical subspace, are consistant with the field equations. A consistent operator solution with residual gauge degrees of freedom is obtained by solving initial value problems on the light-cones. The construction allows a parton picture although we have a physical vacuum with nontrivial degeneracies in the theory.