Gm. Dariano et Mf. Sacchi, TRACE FORMS FOR THE GENERALIZED WIGNER FUNCTIONS, Nuovo cimento della Societa italiana di fisica. B, Relativity, classical and statistical physics, 112(6), 1997, pp. 881-888
We derive simple formulas connecting the generalized Wigner functions
for s-ordering with the density matrix, and vice versa. These formulas
proved very useful for quantum-mechanical applications, as, for examp
le, for connecting master equations with Fokker-Planck equations, or f
or evaluating the quantum state from Monte Carlo simulations of Fokker
-Planck equations, and finally for studying positivity of the generali
zed Wigner functions in the complex plane.