Clifford Algebras and their Applications in Mathematical Physics: Volume 1: Algebra and Physics
Gespeichert in:
| Weitere Verfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2000
|
| Schriftenreihe: | Progress in Physics
18 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) position X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four translation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Poisson bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1 |
| Beschreibung: | 1 Online-Ressource (XXV, 461 p) |
| ISBN: | 9781461213680 9781461271161 |
| DOI: | 10.1007/978-1-4612-1368-0 |
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| 245 | 1 | 0 | |a Clifford Algebras and their Applications in Mathematical Physics |b Volume 1: Algebra and Physics |c edited by Rafał Abłamowicz, Bertfried Fauser |
| 264 | 1 | |a Boston, MA |b Birkhäuser Boston |c 2000 | |
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| 490 | 1 | |a Progress in Physics |v 18 | |
| 500 | |a The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) position X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four translation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Poisson bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1 | ||
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| id | DE-604.BV042419816 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461213680 9781461271161 |
| language | English |
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| series | Progress in Physics |
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| spelling | Clifford Algebras and their Applications in Mathematical Physics Volume 1: Algebra and Physics edited by Rafał Abłamowicz, Bertfried Fauser Boston, MA Birkhäuser Boston 2000 1 Online-Ressource (XXV, 461 p) txt rdacontent c rdamedia cr rdacarrier Progress in Physics 18 The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) position X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four translation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Poisson bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1 Mathematics Global differential geometry Mathematical physics Differential Geometry Mathematical Methods in Physics Theoretical, Mathematical and Computational Physics Mathematik Mathematische Physik Abłamowicz, Rafał (DE-588)114624917 edt Fauser, Bertfried edt Progress in Physics 18 (DE-604)BV000002074 18 https://doi.org/10.1007/978-1-4612-1368-0 Verlag Volltext |
| spellingShingle | Clifford Algebras and their Applications in Mathematical Physics Volume 1: Algebra and Physics Progress in Physics Mathematics Global differential geometry Mathematical physics Differential Geometry Mathematical Methods in Physics Theoretical, Mathematical and Computational Physics Mathematik Mathematische Physik |
| title | Clifford Algebras and their Applications in Mathematical Physics Volume 1: Algebra and Physics |
| title_auth | Clifford Algebras and their Applications in Mathematical Physics Volume 1: Algebra and Physics |
| title_exact_search | Clifford Algebras and their Applications in Mathematical Physics Volume 1: Algebra and Physics |
| title_full | Clifford Algebras and their Applications in Mathematical Physics Volume 1: Algebra and Physics edited by Rafał Abłamowicz, Bertfried Fauser |
| title_fullStr | Clifford Algebras and their Applications in Mathematical Physics Volume 1: Algebra and Physics edited by Rafał Abłamowicz, Bertfried Fauser |
| title_full_unstemmed | Clifford Algebras and their Applications in Mathematical Physics Volume 1: Algebra and Physics edited by Rafał Abłamowicz, Bertfried Fauser |
| title_short | Clifford Algebras and their Applications in Mathematical Physics |
| title_sort | clifford algebras and their applications in mathematical physics volume 1 algebra and physics |
| title_sub | Volume 1: Algebra and Physics |
| topic | Mathematics Global differential geometry Mathematical physics Differential Geometry Mathematical Methods in Physics Theoretical, Mathematical and Computational Physics Mathematik Mathematische Physik |
| topic_facet | Mathematics Global differential geometry Mathematical physics Differential Geometry Mathematical Methods in Physics Theoretical, Mathematical and Computational Physics Mathematik Mathematische Physik |
| url | https://doi.org/10.1007/978-1-4612-1368-0 |
| volume_link | (DE-604)BV000002074 |
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