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Topics in infinite dimensional analysis

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Mathematical Problems in Theoretical Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 80))

Abstract

We present some recent results in three different but connected domains of infinite dimentional analysis. In chapter I we report on work concerning the homogeneous generalized random fields of constructive quantum field theory. In particular a Dynkin entrance boundary construction is given and the global Markov property of the boundary measures is discussed. The connection of these fields with the general theory of Dirichlet forms and diffusion processes on rigged Hilbert spaces is shortly described. In chapter II we report on the energy representation of Sobolev--Lie groups. These groups are defined as completions in the energy metric of the groups of C1-mappings from Riemann manifolds into Lie groups of compact type. The energy representation extends the one given by Euclidean Markov fields to the case of fields with values in a Lie group. In chapter III we report on results concerning oscillatory integrals in infinitely many dimensions and their asymptotic expansions, with applications to the Feynman path integrals and the approach to the classical limit of quantum mechanics.

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Authors and Affiliations

  1. Matematisk Institutt, Universitetet i Oslo, Norway

    Sergio Albeverio & Raphael Høegh-Xrohn

  2. Zentrum für interdisziplinäre Forschung, Universität Bielefeld, Germany

    Sergio Albeverio & Raphael Høegh-Xrohn

Authors
  1. Sergio Albeverio
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  2. Raphael Høegh-Xrohn
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G. Dell'Antonio S. Doplicher G. Jona-Lasinio

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© 1978 Springer-Verlag

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Albeverio, S., Høegh-Xrohn, R. (1978). Topics in infinite dimensional analysis. In: Dell'Antonio, G., Doplicher, S., Jona-Lasinio, G. (eds) Mathematical Problems in Theoretical Physics. Lecture Notes in Physics, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08853-9_23

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  • DOI: https://doi.org/10.1007/3-540-08853-9_23

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  • Online ISBN: 978-3-540-35811-4

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