ON THE QUANTUM DEFORMATIONS OF HAMILTONIAN-SYSTEMS

In this paper we analyze the relationship between operatorial quantiza tion and deformation quantization for Hamiltonian systems on R(2n). We define heuristically generalized symbols for the operators, which mak e this connection. We construct explicitly deformations which are not equivalent to the Moyal one and show that an infinitesimal, classical canonical transformation does not change the equivalence class of the deformation. The results are applied to the quantum integrability of s ome two dimensional Hamiltonian systems. (C) 1996 American Institute o f Physics.