Dynamics of the Light-Cone Zero Modes: Theta Vacuum of the Massive Schwinger Model

TL;DR

This paper investigates the dynamics of zero modes in the massive Schwinger model quantized on the light cone, revealing how the theta vacuum emerges as a Bloch momentum and analyzing the vacuum and meson states.

Contribution

It provides a detailed analysis of light-cone zero modes and the theta vacuum in the massive Schwinger model, including the construction of the vacuum and meson states.

Findings

The vacuum is described by a Schrödinger equation with a periodic potential.

The theta parameter acts as a Bloch momentum in the zero-mode dynamics.

A Schrödinger equation for the one-meson state is derived.

Abstract

The massive Schwinger model is quantized on the light cone with great care on the bosonic zero modes by putting the system in a finite (light-cone) spatial box. The zero mode of $A_{-}$ survives Dirac's procedure for the constrained system as a dynamical degree of freedom. After regularization and quantization, we show that the physical space condition is consistently imposed and relates the fermion Fock states to the zero mode of the gauge field. The vacuum is obtained by solving a Schr\"odinger equation in a periodic potential, so that the theta is understood as the Bloch momentum. We also construct a one-meson state in the fermion-antifermion sector and obtained the Schr\"odinger equation for it.