Contracting the Wigner-Kernel of a Spin to the Wigner-Kernel of a Particle

A general relation between the Moyal formalisms for a spin and a particle is established. Once the formalism has been set up for a spin, the phase-space description of a particle is obtained from the `contraction' of the group of rotations to the group of translations. This is shown by explicitly contracting a spin Wigner-kernel to the Wigner kernel of a particle. In fact, only one out of 2^{2s} different possible kernels for a spin shows this behaviour.