A Hamiltonian formalism for classical systems interacting with quantum systems

We propose a general framework of the combined description of a classical s ystem with a quantum system by representing the quantum system as a Hamilto nian field and defined the evolution of the whole system as Hamiltonian flo w. We illustrate the general formalism in two cases, namely the classical p article coupled with a quantum oscillator and classical particle with quant um spin in electromagnetic field.