Vr. Vieira et Pd. Sacramento, CLOSED-FORM RELATIONS FOR PHASE-SPACE REPRESENTATIVES OF SPIN-J OPERATORS, Journal of physics. A, mathematical and general, 27(20), 1994, pp. 120000783-120000788
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.