21 July 2022, 13:15 (EET), Hall 300, INRNE

• Prof. Svetoslav Zahariev (City University of New York, USA)
• Title: Set-Indexed Random Fields and Euclidean Quantum Field Theory
• Abstract: In the standard approach to Euclidean Quantum Field Theory (QFT) one obtains quantum fields from probability measures defined on suitable spaces of distributions via taking ultraviolet/continuum limit. I will present an alternative approach which allows one to construct non-Gaussian probability measures on the space of continuous functions on the space of all balls in Euclidean space of any dimension. These measures induce nets of operator algebras satisfying a version of the Haag-Kastler axioms of Algebraic QFT and may be interpreted as (nonlinear) continuous transformations of the free scalar massive Euclidean quantum field. Time permitting, I will also discuss how the Haag-Ruelle theory of particle scattering may be adapted to this setting.
• Slides