Weyl–Wigner–Moyal formalism for Fermi classical systems

The Weyl–Wigner–Moyal formalism of fermionic classical systems with a finite number of degrees of freedom is considered. The Weyl correspondence is studied by computing the relevant Stratonovich–Weyl quantizer. The Moyal ★-product, Wigner functions and normal ordering are obtained for generic fermionic systems. Finally, this formalism is used to perform the deformation quantization of the Fermi oscillator and the supersymmetric quantum mechanics.