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.