κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
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| Creator |
Borowiec, A.
Pachol, A. |
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| Description |
Some classes of Deformed Special Relativity (DSR) theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl-Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies κ-Minkowski spacetime coordinates with Poincaré generators, can be obtained by nonlinear change of generators from undeformed one. Its various realizations in terms of the standard (undeformed) Weyl-Heisenberg algebra opens the way for quantum mechanical interpretation of DSR theories in terms of relativistic (Stückelberg version) Quantum Mechanics. On this basis we review some recent results concerning twist realization of κ-Minkowski spacetime described as a quantum covariant algebra determining a deformation quantization of the corresponding linear Poisson structure. Formal and conceptual issues concerning quantum κ-Poincaré and κ-Minkowski algebras as well as DSR theories are discussed. Particularly, the so-called ''q-analog'' version of DSR algebra is introduced. Is deformed special relativity quantization of doubly special relativity remains an open question. Finally, possible physical applications of DSR algebra to description of some aspects of Planck scale physics are shortly recalled.
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| Date |
2019-02-09T19:48:57Z
2019-02-09T19:48:57Z 2010 |
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| Type |
Article
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| Identifier |
κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems / A. Borowiec, A. Pachol // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 88 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 16T05; 17B37; 46L65; 53D55; 81R50; 81R60; 81T75; 83C65 DOI:10.3842/SIGMA.2010.086 http://dspace.nbuv.gov.ua/handle/123456789/146520 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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