Noncommutative Lagrange Mechanics
It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy, which are extensively applied within nonc...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149039 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Noncommutative Lagrange Mechanics / D. Kochan // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 13 назв. — англ. |
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Kochan, D. 2019-02-19T13:12:28Z 2019-02-19T13:12:28Z 2008 Noncommutative Lagrange Mechanics / D. Kochan // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 13 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 70G45; 46L55; 53B05 https://nasplib.isofts.kiev.ua/handle/123456789/149039 It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy, which are extensively applied within noncommutative quantum theories. Newton-Lagrange noncommutative equations of motion are formulated and their properties are analyzed from the pure geometrical point of view. It is argued that the dynamical quintessence of the system consists in its kinetic energy (Riemannian metric) specifying Riemann-Levi-Civita connection and thus the inertia geodesics of the free motion. Throughout the paper, ''noncommutativity'' is considered as an internal geometric structure of the configuration space, which can not be ''observed'' per se. Manifestation of the noncommutative phenomena is mediated by the interaction of the system with noncommutative background under the consideration. The simplest model of the interaction (minimal coupling) is proposed and it is shown that guiding affine connection is modified by the quadratic analog of the Lorentz electromagnetic force (contortion term). This paper is a contribution to the Proceedings of the 3-rd Microconference “Analytic and Algebraic Methods III”. This research was supported in part by MSMT ˇ CR grant LC06002, ESF projects: JPD 3 2005/NP1-013 and JPD 3BA 2005/1-034 and VEGA Grant 1/3042/06. The author is thankful to Pavel Exner, Miloslav Znojil and Jaroslav Dittrich for their kindness and hospitality during the author’s short-time fellowship at the Doppler Institute in the autumn 2006. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Noncommutative Lagrange Mechanics Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Noncommutative Lagrange Mechanics |
| spellingShingle |
Noncommutative Lagrange Mechanics Kochan, D. |
| title_short |
Noncommutative Lagrange Mechanics |
| title_full |
Noncommutative Lagrange Mechanics |
| title_fullStr |
Noncommutative Lagrange Mechanics |
| title_full_unstemmed |
Noncommutative Lagrange Mechanics |
| title_sort |
noncommutative lagrange mechanics |
| author |
Kochan, D. |
| author_facet |
Kochan, D. |
| publishDate |
2008 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy, which are extensively applied within noncommutative quantum theories. Newton-Lagrange noncommutative equations of motion are formulated and their properties are analyzed from the pure geometrical point of view. It is argued that the dynamical quintessence of the system consists in its kinetic energy (Riemannian metric) specifying Riemann-Levi-Civita connection and thus the inertia geodesics of the free motion. Throughout the paper, ''noncommutativity'' is considered as an internal geometric structure of the configuration space, which can not be ''observed'' per se. Manifestation of the noncommutative phenomena is mediated by the interaction of the system with noncommutative background under the consideration. The simplest model of the interaction (minimal coupling) is proposed and it is shown that guiding affine connection is modified by the quadratic analog of the Lorentz electromagnetic force (contortion term).
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149039 |
| citation_txt |
Noncommutative Lagrange Mechanics / D. Kochan // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 13 назв. — англ. |
| work_keys_str_mv |
AT kochand noncommutativelagrangemechanics |
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2025-12-07T18:56:31Z |
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2025-12-07T18:56:31Z |
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1850876931092774912 |