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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.
MSC:
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
References:
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