Communications in Mathematical Physics

, Volume 132, Issue 1, pp 39–71 | Cite as

Construction of convergent simplicial approximations of quantum fields on Riemannian manifolds

  • Sergio Albeverio
  • Boguslav Zegarlinski


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.


Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Sergio Albeverio
    • 1
    • 2
  • Boguslav Zegarlinski
    • 1
    • 2
  1. 1.Fakultät für MathematikRuhr-UniversitätBochumFederal, Republic of Germany
  2. 2.SFBBochum-Essen-Düsseldorf

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