  In the operatorial formulation of quantum statistics, the time evolution of
density matrices is governed by von Neumann's equation. Within the phase space
formulation of quantum mechanics it translates into Moyal's equation, and a
formal solution of the latter is provided by Marinov's path integral. In this
paper we uncover a hidden property of the Marinov path integral, demonstrating
that it describes a theory of ruled random surfaces in phase space.
