  A formulation of quantum-classical hybrid dynamics is presented, which
concerns the direct coupling of classical and quantum mechanical degrees of
freedom. It is of interest for applications in quantum mechanical approximation
schemes and may be relevant for the foundations of quantum mechanics, in
particular, when it comes to experiments exploring the quantum-classical
border. The present linear theory differs from the nonlinear ensemble theory of
Hall and Reginatto, but shares with it to fullfill all consistency requirements
discussed in the literature, while earlier attempts failed in this respect. Our
work is based on the representation of quantum mechanics in the framework of
classical analytical mechanics by A. Heslot, showing that notions of states in
phase space, observables, Poisson brackets, and related canonical
transformations can be naturally extended to quantum mechanics. This is
suitably generalized for quantum-classical hybrids here.
