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An analogue of the Heisenberg uncertainty relation in prequantum classical field theory
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics. (ICMM)ORCID iD: 0000-0002-9857-0938
2010 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 81, no 6, p. Article ID: 065001-Article in journal (Refereed) Published
Abstract [en]

Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility of representing averages of quantum observables, including correlations of observables on subsystems of a composite system, as averages with respect to fluctuations of classical random fields. PCSFT is a classical model of wave type. For example, 'electron' is described by electronic field. In contrast to quantum mechanics (QM), this field is a real physical field and not a field of probabilities. An important point is that the prequantum field of, for example, an electron contains the irreducible contribution of the background field vacuum fluctuations. In principle, the traditional QM-formalism can be considered as a special regularization procedure: subtraction of averages with respect to vacuum fluctuations. In this paper, we derive a classical analogue of the Heisenberg-Robertson inequality for dispersions of functionals of classical (prequantum) fields. The PCSFT Robertson-like inequality provides a restriction on the product of classical dispersions. However, this restriction is not so rigid as in QM.

Place, publisher, year, edition, pages
2010. Vol. 81, no 6, p. Article ID: 065001-
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-7297DOI: 10.1088/0031-8949/81/06/065001OAI: oai:DiVA.org:lnu-7297DiVA, id: diva2:343617
Available from: 2010-08-14 Created: 2010-08-14 Last updated: 2017-12-12Bibliographically approved

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Khrennikov, Andrei

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