QUANTIZATION OF MONOTONIC TWIST MAPS

Using an approach suggested by Moser, classical Hamiltonians are gener ated that provide an interpolating flow to the stroboscopic motion of maps with a monotonic twist condition. The quantum properties of these Hamiltonians are then studied in analogy with recent work on the semi classical quantization of systems based on Poincare surfaces of sectio n. For the generalized standard map, the correspondence with the usual classical and quantum results is shown, and the advantages of the qua ntum Moser Hamiltonian demonstrated. The same approach is then applied to the free motion of a particle on a 2-torus, and to the circle bill iard. A natural quantization condition based on the eigenphases of the unitary time-development operator is applied, leaving the exact eigen values of the torus, but only the semiclassical eigenvalues for the bi lliard; an explanation for this failure is proposed. It is also seen h ow iterating the classical map commutes with the quantization.