Kisil, V orcid.org/0000-0002-6593-6147 (2017) Symmetry, Geometry and Quantization with Hypercomplex Numbers. Geometry, Integrability and Quantization, 18. pp. 11-76. ISSN 1314-3247
Abstract
These notes describe some links between the group SL2(R), the Heisenberg group and hypercomplex numbers - complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this framework. In particular, classical mechanics can be obtained as a theory with noncommutative observables and a non-zero Planck constant if we replace complex numbers in quantum mechanics by dual numbers. Our consideration is based on induced representations which are build from complex-/dual/-double-valued characters. Dynamic equations, rules of additions of probabilities, ladder operators and uncertainty relations are also discussed. Finally, we prove a Calderón-Vaillancourt-type norm estimation for relative convolutions.
Metadata
Item Type: | Article |
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Authors/Creators: | |
Keywords: | math-ph; math-ph; math.CV; math.MP; math.RT; quant-ph; 81P05, 22E27 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 02 Feb 2017 09:39 |
Last Modified: | 04 Dec 2018 09:56 |
Status: | Published |
Publisher: | Bulgarian Academy of Sciences |
Identification Number: | 10.7546/giq-18-2017-11-76 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111547 |