Maslov Phase as Geometric Phase in the Time-Dependent Variational Approach with Squeezed Coherent States

Abstract

Toward the classical description of quantum fluctuations in quantal systems, the Maslov phase occurring in a semi-classical quantization rule is investigated in a framework of the time·dependent variational principle with squeezed coherent states. In the limit of a semi-classical approximation in this approach, it is definitely shown that the Maslov phase has a geometric nature analogous to Berry's phases or canonical phases including dynamical effects. The Maslov phase appears as a winding number in this framework. It is also indicated that this squeezed coherent state approach is a possible way to go beyond the usual WKB approximation.