Phase-space representation for Galilean quantum particles of arbitrary spin

The phase-space approach to quantisation is extended to incorporate spinning particles with Galilean symmetry. The appropriate phase space is the coadjoint orbit r 6 *S 2 . From two basic principles, traciality and Galilean covariance, the Weyl symbol calculus is constructed. Then the Galilean-equivariant twisted products of functions on this phase space are identified.