QUASI-CLASSICAL DESCRIPTIONS OF QUANTUM-SYSTEMS BASED ON COHERENT STATES - PRODUCT-FORMULAS

If the state space of a quantum system is finite dimensional it may be considered as the carrier space of an irreducible unitary representation of some compact Lie group G. In this case the set of operators may be put in one-to-one correspondence with a class of functions defined on the group parameters (Q representation). For these functions a binary relation is derived that corresponds to the product of two operators. The general formalism is applied to G=SU(2) (spin coherent states) and this result is used to derive a product formula for the non-compact Heisenberg-Weyl group (coherent oscillator states.).