Stargenfunctions, generally parametrized systems and a causal   formulation of phase space quantum mechanics
  We address the deformation quantization of generally parametrized systems displaying a natural time variable. The purpose of this exercise is twofold: first, to illustrate through a pedagogical example the potential of quantum phase space methods in the context of constrained systems and particularly of generally covariant systems. Second, to show that a causal representation for quantum phase space quasidistributions can be easily achieved through general parametrization. This result is succinctly discussed. 
Nuno Costa Dias, Joao Nuno Prata