where r s is a constant related to the radius of the Bloch sphere, and |Ω is the generalized spin-coherent state expressed in Eqs. 17-18. One can clearly see that the S-W kernel depends on both the generators Ŝ of the Lie algebra (represented in the Hilbert space) and the parameters {θ n , ϕ n } of the manifold. Using the spin coherent states, we can also express the S-W kernel in Eq. 26 as 64