within the Coulomb gauge has been studied in [@campos]. Deformation quantization of gravitational field as a constrained system has been discussed in [@antonu; @antond]. Then the linearized gravitational field from the point of view of deformation quantization has been described in [@hquevedo]. It is worth while to note that also perturbation quantum field theory can be given the form of deformation quantization formalism [@paftadq; @ditofour; @pqft]. Moreover, as has been shown in [@strings] deformation quantization theory can be applied to quantize the classical bosonic strings in the light-cone gauge. On the other hand, string theory uses also the deformation quantization formalism (WWM-formalism) to describe the spacetime worldvolume of a D-brane. The presence of a non-zero constant $B$-field on the worldvolume deforms the product of functions (or classical fields) on the D-brane into a Moyal $\star$-product, and the ordinary effective field theory on the D-brane turns into a noncommutative field theory with this Moyal $\star$-product [@sw].

Most of the cases studied by the deformation quantization for systems with a finite number of degrees of freedom deal with bosonic variables. However, the analysis of some classical physical systems requires the description of fermionic degrees of freedom which involve Grassmann variables. These systems 