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Measures on Hilbert-Schmidt operators and algebraic quantum field theory

2016/03/14 by Svetoslav Zahariev, Zahariev, Svetoslav
Mathematics · Physics and Astronomy · #81T05 #81T08 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.1603.04371

openalex publication_date 2016/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a general construction of non-Gaussian probability measures on the space of distributional kernels obeying a natural extension of the Osterwalder-Schrader axioms of Euclidean quantum field theory in arbitrary space-time dimension d. These measures may be interpreted as corresponding to scalar massive quantum fields with polynomial self-interaction. As a consequence, we obtain examples of non-free models satisfying the Haag-Kastler axioms of algebraic quantum field theory for arbitrary d. When d<4 we are able to transfer the measures to the space of distributions and verify the standard Osterwalder-Schrader axioms, hence, by a well-known reconstruction theorem, we also obtain quantum field theory models satisfying the axioms of Wightman.

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