Title:   On Smooth Measures in ``Infinite Dimensional Analysis''
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ABSTRACT:
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This talk will describe some smoothness and function analytic
properties of certain natural measures on path and loop spaces of
compact Riemannian manifolds and compact Lie groups. The study of
these questions is motivated, in part, by problems in physics
relating to the path integral interpretation of quantum mechanics.
I will briefly describe some (or at least one) such problems. Of
course ``functional integration methods'' in the context of
quantum field theory is responsible for a number of interesting
mathematical conjectures. Although I may touch on one such
conjecture, the talk will concentrate on what can be said in the
more mathematically tractable setting of path and loop spaces of
finite dimensional manifolds.