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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, article id 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, article id 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, id: diva2:640859
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Mathematical ModelingAvailable from: 2013-08-14 Created: 2013-08-14 Last updated: 2017-12-06Bibliographically approved

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Khrennikov, Andrei

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