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The Schrödinger-Robinson inequality from stochastic analysis on a complex Hilbert space
Linnaeus University, Faculty of Technology, Department of Mathematics. Russian State Univ Humanities, Russia. (mathematics)ORCID iD: 0000-0002-9857-0938
2013 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 87, no 3, 038109Article in journal (Refereed) Published
Abstract [en]

We explored the stochastic analysis on a complex Hilbert space to show that one of the cornerstones of quantum mechanics (QM), namely Heisenberg's uncertainty relation, can be derived in the classical probabilistic framework. We created a new mathematical representation of quantum averages: as averages with respect to classical random fields. The existence of a classical stochastic model matching with Heisenberg's uncertainty relation makes the connection between classical and quantum probabilistic models essentially closer. In real physical situations, random fields are valued in the L2-space. Hence, although we model QM and not QFT, the classical systems under consideration have an infinite number of degrees of freedom. And in our modeling, infinite-dimensional stochastic analysis is the basic mathematical tool.

Place, publisher, year, edition, pages
2013. Vol. 87, no 3, 038109
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-28160DOI: 10.1088/0031-8949/87/03/038109ISI: 000315194000031OAI: oai:DiVA.org:lnu-28160DiVA: diva2:640859
Projects
Mathematical Modeling
Available from: 2013-08-14 Created: 2013-08-14 Last updated: 2017-12-06Bibliographically approved

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Khrennikov, Andrei

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