  We consider spin system defined on the coadjoint orbit with noncompact
symmetry and investigate the quantization. Classical spin with noncompact
SU(N,1) symmetry is first formulated as a dynamical system and the constraint
analysis is performed to reduce the system from the group space to the
coadjoint orbit which is a symplectic manifold with Kahler structure. We
achieve this by solving the constraint directly. It is shown that the dynamical
variables describing the noncompact spins can be written as functions of
canonically conjugate variables and canonical quantization is possible on the
reduced phase space. With the quantum mechanical Hamiltonian acting on the
holomorphic coherent state in Hilbert space, we obtain the exact propagator by
solving the time-dependent Schrodinger equation.
