  Motivated by certain concepts introduced by the Refined Algebraic
Quantization formalism for constrained systems which has been successfully
applied within the context of Loop Quantum Gravity, in this paper we propose a
phase space implementation of the Dirac quantization formalism to appropriately
include systems with constraints. In particular, we propose a physically
prescribed Wigner distribution which allows the definition of a well-defined
inner product by judiciously introducing a star version of the group averaging
of the constraints. This star group averaging procedure is obtained by
considering the star-exponential of the constraints and then integrating with
respect to a suitable measure. In this manner, the proposed physical Wigner
distribution explicitly solves the constraints by including generalized
functions on phase space. Finally, in order to illustrate our approach, our
proposal is tested in a couple of simple examples which recover standard
results found in the literature.
