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Construction of convergent simplicial approximations of quantum fields on Riemannian manifolds. (English) Zbl 0708.60101
Summary: We construct simplicial approximations of random fields on Riemannian manifolds of dimension d. We prove convergence of the fields to the continuum limit, for arbitrary d in the Gaussian case and for d=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.
60K40Physical applications of random processes
81T20Quantum field theory on curved space backgrounds
58E15Applications of variational methods to extremal problems in several variables; Yang-Mills functionals
58C99Calculus on manifolds
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