A GENERAL FORMULATION OF DISCRETE-TIME QUANTUM-MECHANICS - RESTRICTIONS ON THE ACTION AND THE RELATION OF UNITARITY TO THE EXISTENCE THEOREM FOR INITIAL-VALUE PROBLEMS

A general formulation for discrete-time quantum mechanics, based on Fe ynman's method in ordinary quantum mechanics, is presented. It is show n that the ambiguities present in ordinary quantum mechanics (due to n oncommutativity of the operators), are no longer present here. Then th e criteria for the unitarity of the evolution operator are examined. I t is shown that the unitarity of the evolution operator puts restricti ons on the form of the action, and also implies the existence of a sol ution for the classical initial-value problem. (C) 1995 Academic Press , Inc.