Chiral bosons and improper constraints

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 condition defines a problem which must be treated separately. 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 antiperiodic boundary conditions, the model 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 Poincare symmetry holds for the finite as well as for the infinite domain.