Generalized phase-space representatives of spin-J operators in terms of Bloch coherent states

The c-number functions corresponding to the matrix elements and to the diagonal representative of the elements of the spin-J representation of the rotation group in a Bloch coherent state basis are obtained in closed form. The matrix element and the diagonal representative of the spin-J representation are simply the power 2J and 2(J+1)/3 of those of the spin-1/2 case, respectively. We obtain the representatives of any spin operator by differentiation of the properly ordered exponential operators. Our methods simplify the calculations, avoiding the introduction of Schwinger bosons and the consequent projection to the physical subspace. In particular, we obtain several product theorems for the representatives of two or more operators. Use of the rotated spherical basis vectors allows us to write the representatives of the cumulants of spin operators in a compact form. In particular, the lowest three take a factorized form. Introducing the holomorphic representation, we obtain the diagonal representative from the diagonal matrix element as an integral relation without recurring to expansions in spherical harmonics. Introducing a generalized Fourier transformation in spin-J space in a way similar to the treatment by Cahill and Glauber of the boson coherent states, new analogies between the two sets of coherent states are established. Using its inversion properties we obtain in closed form relations between the c-number functions which represent an operator in spin-J space. Also, we study the generalization to the spin case of the s-ordering of Cahill and Glauber interpolating between the diagonal matrix element and the diagonal representative. Copyright copyright 1995 Academic Press, Inc