Extensions of Wigner’s distribution to particles with spin 1/2

For particles of spin 1/2 a class of distributions closely related to Wigner’s is introduced on dynamical grounds. It is found that they may be refined to give correct expectation values of higher powers of spin components, but depart somewhat from a criterion that has been used in characterizing the Wigner distribution. For a special choice amongst this class, a more subtle refinement is possible satisfying this criterion exactly. This requires, however, a dubious distinction at every point between positive spin about a direction and negative spin about the reverse direction.