Set-indexed random fields and algebraic Euclidean quantum field theory

2021/08/30 by Svetoslav Zahariev, Zahariev, Svetoslav
Mathematics · #Probability and Statistical Research #Mathematical and Theoretical Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2108.13443

Abstract

We present a construction of non-Gaussian Borel measures on the space of continuous functions defined on the space of all balls in Euclidean space of arbitrary dimension. These measures induce nets of operator algebras satisfying the Haag-Kastler axioms of algebraic quantum field theory and may be interpreted as (nonlinear) continuous transformations of the free scalar massive Euclidean quantum field.

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