In this paper we report a new method for resummation of operator expansions of the evolution operator. These resummation techniques are applied to the Feynman propagator and then to the derivation of an effective Schrouml;dinger equation for general systemndash;bath problems. This paper presents a significant advance over work previously reported by us lsqb;J. Chem. Phys.96, 5952 (1992)rsqb;, and it provides a highly accurate way to calculate quantum mechanical data for many dimensional systems. We then apply this new analytic resummation technique to the calculation of fluxndash;flux correlation functions for two, three, and four dimensional problems in order to study the range of applicability of the approach. For moderate frequencies and coupling strengths, not only is the resummed operator calculational method essentially exact, it also requires a fraction of the computer time that the exact calculation consumes. For truly many dimensional problems this approach should provide the first accurate quantum mechanics of rate processes.
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