  We develop a so-called theory of ensembles in phase space and use it to
investigate the construction of a quantum-classical hybrid theory. We use
Galilei covariance and the Lie algebra of the Galilei group as a guide to
constructing the hybrid model presented here. In particular, we chose the
interaction term between the classical and the quantum sector so that the
equations are Galilei covariant. Our approach points out a possible connection
between two previously unrelated hybrid systems.
