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p-Adic valued quantization
Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. (Mathematics)ORCID iD: 0000-0002-9857-0938
2009 (English)In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 1, no 2, p. 91-104Article, review/survey (Refereed) Published
Abstract [en]

This review covers an important domain of p-adic mathematical physics — quantum mechanics with p-adic valued wave functions. We start with basic mathematical constructions of this quantum model: Hilbert spaces over quadratic extensions of the field of p-adic numbers ℚ p , operators — symmetric, unitary, isometric, one-parameter groups of unitary isometric operators, the p-adic version of Schrödinger’s quantization, representation of canonical commutation relations in Heisenberg andWeyl forms, spectral properties of the operator of p-adic coordinate.We also present postulates of p-adic valued quantization. Here observables as well as probabilities take values in ℚ p . A physical interpretation of p-adic quantities is provided through approximation by rational numbers.

Place, publisher, year, edition, pages
Berlin: Springer , 2009. Vol. 1, no 2, p. 91-104
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:vxu:diva-7124DOI: 10.1134/S2070046609020010OAI: oai:DiVA.org:vxu-7124DiVA, id: diva2:293984
Available from: 2010-02-15 Created: 2010-02-15 Last updated: 2017-12-12Bibliographically approved

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Publisher's full texthttp://www.springerlink.com/content/u75135874h30/?p=8cd9169bf5b247fe8485fc7b21f64c03&pi=3

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Khrennikov, Andrei

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