have been discussed in the literature for several years [@berezinbook; @casa; @marinov; @sberezin; @dewittbook; @susyqmb]. (Some extension of the WWM formalism to infinite degrees of freedom for fermions can also be found in [@bereone; @beretwo; @schmutz]). The canonical quantization of the fermionic systems by using the Grassmann variables has been studied in all detail in [@marnelius]. Very recently some authors started to apply the machinery of deformation quantization to quantize the classical fermionic systems [@bordemann; @bordemannII; @hirshfeld; @duetsch; @zachosfermions; @clifford]. In particular, in [@hirshfeld; @imelda] it has been shown concretely how the deformation quantization program can be carried over to specific physical fermionic systems. The same techniques have been applied recently for the noncommutative superspace [@seiberg].

In the present paper we study the canonical approach to deformation quantization for fermionic fields by employing the traditional Weyl-Wigner-Moyal correspondence [@wwmformalism; @tata; @hillery]. To this end we extend the results obtained in the previous paper [@imelda] in the context of fermionic systems with a finite number of degrees of freedom. We deal with the Dirac free field and reproduce several results about its quantization and its Green’s functions.

Our paper is organized as follows. Sec. \[scalar\_field\] is devoted to deformation quantization of a 