Do half integer spin fields commute or anti-commute with spin integer fields?

Question

What are the fundamental commutation/anti-commutation relations between half integer and integer spin fields? For instance, in QED do we have \begin{equation} [\psi(x),A^{\mu}(y)]=0 \end{equation} or \begin{equation} \lbrace\psi(x),A^{\mu}(y)\rbrace=0 \end{equation} ?

Answer 1

They commute; see e.g. this discussion of the $\mathbb{Z}_2$ grading involved.