J. Wilkie et P. Brumer, Transformation theory for phase-space representations of quantum mechanics- art. no. 064101, PHYS REV A, 6106(6), 2000, pp. 4101
Dirac bras and kets are explicitly defined for phase-space representations
of quantum mechanical observables, and simple transformation rules for chan
ging representations are constructed. Derivations in the Wigner-Weyl repres
entation of an expression for the kernel of the quantum Liouville operator,
and of a relation between its stationary and nonstationary eigenstates, de
monstrate the power of the resultant algebra.