Light-front Quantized Chiral Schwinger Model and its Vacuum Structure

TL;DR

This paper quantizes the bosonized Chiral Schwinger model on the light-front, clarifying its vacuum structure, differences from the Schwinger model, and demonstrating the equivalence of light-front and conventional quantization methods.

Contribution

It provides a direct light-front quantization of the bosonized Chiral Schwinger model, elucidating its vacuum structure and differences from the Schwinger model.

Findings

Vacuum structure of the CSM is clarified without $ heta$-vacua.

LF quantization results agree with conventional methods.

Differences in mass excitations and vacua are transparently displayed.

Abstract

The bosonized Chiral Schwinger model (CSM) is quantized on the light-front (LF). The physical Hilbert space of CSM is obtained directly once the constraints on the LF phase space are eliminated. The discussion of the degenerate vacua and the absence in the CSM of the $\theta$-vacua, as found in the Schwinger model (SM), becomes straightforward. The differences in the structures of the the mass excitations and the vacua in these gauge theories are displayed transparently. The procedure followed is the one used successfully in the previous works for describing the spontaneous symmetry breaking (SSB) and the SM on the LF. The physical contents following from the LF quantized theory agree with those known in the conventional treatment. The LF hyperplane is argued to be equally appropriate as the conventional equal-time one for the canonical quantization. Some comments on the irrelevance, in quantized field theory, of the fact that the hyperplanes $x^{\pm}=0$ constitute characteristic surfaces of hyperbolic partial differential equation are also made.