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Diffusions, quantum fields and groups of mappings

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Functional Analysis in Markov Processes

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 923))

Abstract

We discuss some relations between the theory of symmetric Markov processes and homogeneous Markov fields and the theory of representations of the groups of mappings of a manifold into a compact Lie group.

In this lecture we shall discuss on one hand some new developments in the theory of homogeneous Markov random fields and on the other hand a non commutative extension of these, with applications to the representation theory of groups of mappings. The unification is obtained by looking at both the commutative and non commutative cases as representations of the groups of mappings of a Riemannian manifold X into a Lie group G.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Ruhr-Universität Bochum, 4630, Bochum 1, Germany

    Sergio Albeverio

  2. Matematisk Institutt, Universitetes i Oslo, Blindern, Oslo 3, Norway

    Raphael Høegh-Krohn

Authors
  1. Sergio Albeverio
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  2. Raphael Høegh-Krohn
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M. Fukushima

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© 1982 Springer-Verlag

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Albeverio, S., Høegh-Krohn, R. (1982). Diffusions, quantum fields and groups of mappings. In: Fukushima, M. (eds) Functional Analysis in Markov Processes. Lecture Notes in Mathematics, vol 923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093039

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  • DOI: https://doi.org/10.1007/BFb0093039

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  • Print ISBN: 978-3-540-11484-0

  • Online ISBN: 978-3-540-39155-5

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