PATH-INTEGRAL QUANTIZATION AND RIEMANNIAN-SYMPLECTIC MANIFOLDS

We develop a mathematically well-defined path integral formalism for g eneral symplectic manifolds. We argue that in order to make a path int egral quantization covariant under general coordinate transformations on the phase space and involve a genuine functional measure that is bo th finite and countably additive, the phase space manifold should be e quipped with a Riemannian structure (metric). A suitable method to cal culate the metric is also proposed. (C) 1998 Published by Elsevier Sci ence B.V. All rights reserved.