---
abstract: 'Deformation quantization for any Grassmann scalar free field is described via the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal $\star$-product and the Wigner functional are obtained by extending the formalism proposed recently in [@imelda] to the fermionic systems of infinite number of degrees of freedom. In particular, this formalism is applied to quantize the Dirac free field. It is observed that the use of suitable oscillator variables facilitates considerably the procedure. The Stratonovich-Weyl quantizer, the Moyal $\star$-product, the Wigner functional, the normal ordering operator, and finally, the Dirac propagator have been found with the use of these variables.'
author:
- 'I. Galaviz$^2$, H. García-Compeán$^{1,2}$'
- 'M. Przanowski'
- 'F.J. Turrubiates'
title: Deformation Quantization of Fermi Fields
---

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Introduction
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Deformation quantization is commonly regarded as an alternative approach to quantization. In principle, it can be implemented into any classical system of particles, fields, strings or string fields. This is based on the philosophy of deforming suitable standard mathematical structures. Such a philosophy was introduced in 1978 by Bayen, Flato, Fronsdal, Lichnerowicz and Sternheimer [@bffls] (for a recent account, see [@disq; @reviews]). The deformation quantization formalism has a firm mathematical basis. However, its application to quantize an arbitrary 