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Rate of cluster decomposition via Fermat-Steiner point. (English) Zbl 1415.81034

Summary: In quantum field theory with a mass gap correlation function between two spatially separated operators decays exponentially with the distance. This fundamental result immediately implies an exponential suppression of all higher point correlation functions, but the predicted exponent is not optimal. We argue that in a general quantum field theory the optimal suppression of a three-point function is determined by total distance from the operator locations to the Fermat-Steiner point. Similarly, for the higher point functions we conjecture the optimal exponent is determined by the solution of the Euclidean Steiner tree problem. We discuss how our results constrain operator spreading in relativistic theories.

MSC:

81T10 Model quantum field theories
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
62P35 Applications of statistics to physics
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