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Construction of convergent simplicial approximations of quantum fields on Riemannian manifolds

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Abstract

We construct simplicial approximations of random fields on Riemannian manifolds of dimensiond. We prove convergence of the fields to the continuum limit, for arbitraryd in the Gaussian case and ford=2 in the non-Gaussian case. In particular we obtain convergence of the simplicial approximation to the continuum limit for quantum fields on Riemannian manifolds with exponential interaction.

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Author notes

  1. Sergio Albeverio

    Present address: CERFIM, Locarno

Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität, D-4630, Bochum, Federal, Republic of Germany

    Sergio Albeverio & Boguslav Zegarlinski

  2. SFB, 237, Bochum-Essen-Düsseldorf

    Sergio Albeverio & Boguslav Zegarlinski

Authors
  1. Sergio Albeverio
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  2. Boguslav Zegarlinski
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Communicated by K. Gawedzki

Dedicated to Res Jost and Arthur Wightman

BiBoS Research Centre

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Albeverio, S., Zegarlinski, B. Construction of convergent simplicial approximations of quantum fields on Riemannian manifolds. Commun.Math. Phys. 132, 39–71 (1990). https://doi.org/10.1007/BF02277999

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