REMARKS ON THE QUASI-CLASSICAL PROPAGATOR OF AREA-PRESERVING MAPS

The path-integral-like expression for the quantum propagator of discrete-time area-preserving maps is evaluated approximately by neglecting higher than second-order terms in an expansion of the action about the classical paths. In the resulting quasi-classical approximation for the propagator special attention is paid to the recursive nature of its amplitude and the possible appearance of Maslov-like phases. Using a further approximation for the amplitude we arrive at explicit expressions which clearly show the differences between the contributions of stable and unstable classical paths. An estimate for the range of validity for the quasi-classical approximation is also given.