CHIRAL BOSONS AND IMPROPER CONSTRAINTS

We argue that a consistent quantization of the Floreanini-Jackiw model , as a constrained system, should start by recognizing the improper na ture of the constraints. Then, each boundary condition defines a probl em 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 periodi c boundary conditions the model turns out to be a gauge theory whose g auge invariant sector contains only chiral excitations. For antiperiod ic boundary conditions, the model is a second-class theory where the e xcitations are also chiral. In both cases, the equal-time algebra of t he quantum energy-momentum densities is a Virasoro algebra. The Poinca re symmetry holds for the finite as well as for the infinite domain.