This is something I got curious about. Let's say I have the Wigner function for an $n$ particle system:
$$W \equiv W(x_1,\dots,x_n,;p_1,\dots,p_n) $$
Now, let's say this system obeys has spin. As far as I understand that restricts the allowed eigen-basis (upon interchange of $r_i \leftrightarrow r_j$for bosons its symmetric for fermions it's antisymmetric). Does this have any bearing on the wigner function (Since the Wigner function itself is constructed out of these wavefunctions)? If so, I'm looking for a calculation where the effects of this manifestation disappear under the classical limit $\hbar \to 0$?