Quantization of a classical system on a coadjoint orbit of the Poincaré group in 1+1 dimensions

Abstract

The connection is investigated between quantization by means of coherent states and geometric quantization, when the base manifold is a coadjoint orbit, and hence a homogeneous space, of the (1+1)-dimensional Poincaré group. Coherent states of the Poincaré group stem from a representation that is square-integrable modulo closed subgroup, and so they depend on a measurable section on the given homogeneous space. For each section that leads to a tight frame, a geometric prequantization is constructed, i.e., a Hermitian line bundle with metric connection. Conditions are given under which the two forms associated to the connection and to the coadjoint orbit structure of the base manifold coincide.