κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems

κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems

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, w...

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Бібліографічні деталі
Дата:2010
Автори: Borowiec, A., Pachol, A.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2010
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/146520
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1465202019-02-10T01:25:29Z κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems Borowiec, A. Pachol, A. 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. 2010 Article 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 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 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.
format Article
author Borowiec, A.
Pachol, A.
spellingShingle Borowiec, A.
Pachol, A.
κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Borowiec, A.
Pachol, A.
author_sort Borowiec, A.
title κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
title_short κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
title_full κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
title_fullStr κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
title_full_unstemmed κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
title_sort κ-minkowski spacetimes and dsr algebras: fresh look and old problems
publisher Інститут математики НАН України
publishDate 2010
url http://dspace.nbuv.gov.ua/handle/123456789/146520
citation_txt 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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT borowieca kminkowskispacetimesanddsralgebrasfreshlookandoldproblems
AT pachola kminkowskispacetimesanddsralgebrasfreshlookandoldproblems
first_indexed 2023-05-20T17:24:59Z
last_indexed 2023-05-20T17:24:59Z
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