CLOSED-FORM RELATIONS FOR PHASE-SPACE REPRESENTATIVES OF SPIN-J OPERATORS

By introducing the holomorphic representation we obtain, in closed for m, relations between the c-number functions, which represent an operat or in spin-J space, without recurring to expansions in spherical harmo nics. In particular, we obtain the diagonal representative from the di agonal matrix element through an integral relation. New analogies betw een these and the spin (Bloch) coherent states are established which a void the introduction of Schwinger bosons, and the consequent projecti on to the physical subspace, by introducing a generalized Fourier tran sformation in spin-J space in a way similar to the treatment by Cahill and Glauber for boson coherent states. Also, we study the generalizat ion to the spin case of the s-ordering of Cahill and Glauber.