Quantum systems with finite Hilbert space

Quantum systems with finite Hilbert space are considered, and phase-space methods like the Heisenberg-Weyl group, symplectic transformations and Wigner and Weyl functions are discussed. A factorization of such systems in terms of smaller subsystems, based on the Chinese remainder theorem, is studied. The general formalism is applied to the case of angular momentum. In this context, SU (2) coherent states are used for analytic representations. Links between the theory of finite quantum systems and other fields of research are discussed.