Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

Details Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

2004-03-04

arxiv.org/abs/math-ph/0403004v1

Physics

Mathematical Physics

Scientific paper

10.1134/1.2121916

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points.

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