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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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Інститут математики НАН України
2006
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/146063 |
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irk-123456789-1460632019-02-07T01:23:48Z Non-commutative mechanics in mathematical & in condensed matter physics Horváthy, P.A. 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. 2006 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146063 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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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. |
| format |
Article |
| author |
Horváthy, P.A. |
| spellingShingle |
Horváthy, P.A. Non-commutative mechanics in mathematical & in condensed matter physics Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Horváthy, P.A. |
| author_sort |
Horváthy, P.A. |
| title |
Non-commutative mechanics in mathematical & in condensed matter physics |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT horvathypa noncommutativemechanicsinmathematicalincondensedmatterphysics |
| first_indexed |
2023-05-20T17:23:43Z |
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2023-05-20T17:23:43Z |
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1796153196946653184 |