Light-cone quantization of two dimensional field theory in the path integral approach

TL;DR

This paper develops a light-cone path integral quantization method for two-dimensional field theories, revealing new vacuum structures and excitation rules in models like Thirring and Schwinger, with potential extensions to higher dimensions.

Contribution

It introduces a novel quantization condition in light-cone coordinates and explores its implications for various two-dimensional models, including vacuum structures and excitation constraints.

Findings

Selection rules on excitations in the Thirring model based on coupling.

Double integer vacuum structure in the Schwinger model.

Identification of two distinct chiral Schwinger models, one without a θ-vacuum.

Abstract

A quantization condition due to the boundary conditions and the compatification of the light cone space-time coordinate $x^-$ is identified at the level of the classical equations for the right-handed fermionic field in two dimensions. A detailed analysis of the implications of the implementation of this quantization condition at the quantum level is presented. In the case of the Thirring model one has selection rules on the excitations as a function of the coupling and in the case of the Schwinger model a double integer structure of the vacuum is derived in the light-cone frame. Two different quantized chiral Schwinger models are found, one of them without a $\theta$-vacuum structure. A generalization of the quantization condition to theories with several fermionic fields and to higher dimensions is presented.