Non-commutative mechanics in mathematical & in condensed matter physics
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1). Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ''exotic'' partic...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2006 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146063 |
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| Cite this: | Non-commutative mechanics in mathematical & in condensed matter physics / P.A. Horváthy // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 48 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Horváthy, P.A. 2019-02-06T17:14:29Z 2019-02-06T17:14:29Z 2006 Non-commutative mechanics in mathematical & in condensed matter physics / P.A. Horváthy // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 48 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81V70; 81T75 https://nasplib.isofts.kiev.ua/handle/123456789/146063 Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1). Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ''exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space. This paper is a contribution to the Proceedings of the O’Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 22–24, 2006, Budapest, Hungary). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Non-commutative mechanics in mathematical & in condensed matter physics Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Non-commutative mechanics in mathematical & in condensed matter physics |
| spellingShingle |
Non-commutative mechanics in mathematical & in condensed matter physics Horváthy, P.A. |
| title_short |
Non-commutative mechanics in mathematical & in condensed matter physics |
| title_full |
Non-commutative mechanics in mathematical & in condensed matter physics |
| title_fullStr |
Non-commutative mechanics in mathematical & in condensed matter physics |
| title_full_unstemmed |
Non-commutative mechanics in mathematical & in condensed matter physics |
| title_sort |
non-commutative mechanics in mathematical & in condensed matter physics |
| author |
Horváthy, P.A. |
| author_facet |
Horváthy, P.A. |
| publishDate |
2006 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1). Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ''exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146063 |
| citation_txt |
Non-commutative mechanics in mathematical & in condensed matter physics / P.A. Horváthy // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 48 назв. — англ. |
| work_keys_str_mv |
AT horvathypa noncommutativemechanicsinmathematicalincondensedmatterphysics |
| first_indexed |
2025-12-07T15:34:40Z |
| last_indexed |
2025-12-07T15:34:40Z |
| _version_ |
1850864231094681600 |