The Schwinger Model in Light-Cone Gauge

TL;DR

This paper analyzes the Schwinger model in light-cone gauge, providing explicit diagonalization of the Hamiltonian, spectrum, anomaly, and condensate, with detailed Hilbert space structures and treatment of massless fields.

Contribution

It offers a detailed canonical quantization of the Schwinger model in light-cone gauge, explicitly constructing the transformation to diagonalize the Hamiltonian and analyzing the physical Hilbert space.

Findings

Explicit spectrum and chiral anomaly derived

Chiral condensate correctly obtained in decompactification limit

Hilbert space structures for free and interacting cases fully characterized

Abstract

The Schwinger model, defined in the space interval $-L \le x \le L$, with (anti)periodic boundary conditions, is canonically quantized in the light-cone gauge $A_-=0$ by means of equal-time (anti)commutation relations. The transformation diagonalizing the complete Hamiltonian is explicitly constructed, thereby giving spectrum, chiral anomaly and condensate. The structures of Hilbert spaces related both to free and to interacting Hamiltonians are completely exhibited. Besides the usual massive field, two chiral massless fields are present, which can be consistently expunged from the physical space by means of a subsidiary condition of a Gupta-Bleuler type. The chiral condensate does provide the correct non-vanishing value in the decompactification limit $L \to \infty$.