Kisil, VV orcid.org/0000-0002-6593-6147 (2012) Hypercomplex Representations of the Heisenberg Group and Mechanics. International Journal of Theoretical Physics, 51 (3). pp. 964-984. ISSN 0020-7748
Abstract
In the spirit of geometric quantisation we consider representations of the Heisenberg(–Weyl) group induced by hypercomplex characters of its centre. This allows to gather under the same framework, called p-mechanics, the three principal cases: quantum mechanics (elliptic character), hyperbolic mechanics and classical mechanics (parabolic character). In each case we recover the corresponding dynamic equation as well as rules for addition of probabilities. Notably, we are able to obtain whole classical mechanics without any kind of semiclassical limit ħ→0.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer Science+Business Media, LLC, 2011.This is an author produced version of a article, published in International Journal of Theoretical Physics. Uploaded in accordance with the publisher's self-archiving policy.This is a post-peer-review, pre-copyedit version of an article published in International Journal of Theoretical Physics. The final authenticated version is available online at: https://doi.org/10.1007/s10773-011-0970-0 |
Keywords: | Heisenberg group; Kirillov’s method of orbits; Geometric quantisation; Quantum mechanics; Classical mechanics; Planck constant; Dual numbers; Double numbers; Hypercomplex; Jet spaces; Hyperbolic mechanics; Interference; Segal–Bargmann representation; Schrödinger representation; Dynamics equation; Harmonic and unharmonic oscillator; Contextual probability; PT -symmetric Hamiltonian |
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: | 14 May 2019 08:52 |
Last Modified: | 14 May 2019 08:52 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s10773-011-0970-0 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111314 |