Decomposition of Hilbert space in sets of coherent states

الأصل · EN

Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups. The group SU(2) is studied in particular and the orbit spaces of its j=1/2 and j=1 representations completely determined. The orbits of SU(2) in CPⁿ can be either 2 or 3 dimensional, the first of them being either isomorphic to S² or to RP² and the latter being isomorphic to quotient spaces of RP³. We end with a look from the same perspective to the quantum mechanical space of states in particle mechanics.