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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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2008 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149039 |
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| Цитувати: | Noncommutative Lagrange Mechanics / D. Kochan // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 13 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149039 |
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irk-123456789-1490392019-02-20T01:29:05Z Noncommutative Lagrange Mechanics Kochan, D. 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). 2008 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149039 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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). |
| format |
Article |
| author |
Kochan, D. |
| spellingShingle |
Kochan, D. Noncommutative Lagrange Mechanics Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Kochan, D. |
| author_sort |
Kochan, D. |
| title |
Noncommutative Lagrange Mechanics |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT kochand noncommutativelagrangemechanics |
| first_indexed |
2023-05-20T17:32:03Z |
| last_indexed |
2023-05-20T17:32:03Z |
| _version_ |
1796153513555787776 |