Wigner trajectories and Liouville’s theorem

It is found that, in general, Wigner trajectories satisfy Liouville’s theorem only locally, i.e., for restricted phase space and time domains. This fact limits their possible applications. Examples are provided to visualize the process of creation and destruction of Wigner trajectories. It is argued that Weyl transforms of Heisenberg operators are, however, viable alternatives to Wigner trajectories, even though they do not satisfy Liouville’s theorem either.