Chiral bosons and improper constraints

TL;DR

This paper revisits the quantization of the Floreanini-Jackiw model, emphasizing the importance of recognizing improper constraints, and shows that boundary conditions lead to distinct gauge and second-class theories with chiral excitations.

Contribution

It provides a consistent quantization framework for the model by treating boundary conditions separately, revealing gauge and second-class structures with chiral modes.

Findings

Boundary conditions define separate quantization problems.

Model exhibits gauge invariance with chiral excitations under periodic conditions.

Equal-time algebra forms a Virasoro algebra, preserving Poincaré symmetry.

Abstract

We argue that a consistent quantization of the Floreanini-Jackiw model, as a constrained system, should start by recognizing the improper nature of the constraints. Then each boundary conditon defines a problem which must be treated sparately. The model is settled on a compact domain which allows for a discrete formulation of the dynamics; thus, avoiding the mixing of local with collective coordinates. For periodic boundary conditions the model turns out to be a gauge theory whose gauge invariant sector contains only chiral excitations. For antiperiodoc boundary conditions, the mode is a second-class theory where the excitations are also chiral. In both cases, the equal-time algebra of the quantum energy-momentum densities is a Virasoro algebra. The Poincar\'e symmetry holds for the finite as well as for the infinite domain.