  The Weyl-Wigner-Moyal formalism for Dirac second class constrained systems
has been proposed recently as the deformation quantization of Dirac bracket. In
this paper, after a brief review of this formalism, it is applied to the case
of the relativistic free particle. Within this context, the Stratonovich-Weyl
quantizer, Weyl correspondence, Moyal $\star$-product and Wigner function in
the constrained phase space are obtained. The recent Hamiltonian treatment for
constrained systems, whose constraints depend explicitly on time, are used to
perform the deformation quantization of the relativistic free charged particle
in an arbitrary electromagnetic background. Finally, the system consisting of a
charged particle interacting with a dynamical Maxwell field is quantized in
this context.
