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SIGMA, 2010, том 6, 086, 31 страниц (Mi sigma544)  

Эта публикация цитируется в 36 научных статьях (всего в 36 статьях)

$\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems

Andrzej Borowiec, Anna Pachol

Institute for Theoretical Physics, University of Wroclaw, pl. Maxa Borna 9, 50-204 Wroclaw, Poland

Аннотация: 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 $\kappa$-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 $\kappa$-Minkowski spacetime described as a quantum covariant algebra determining a deformation quantization of the corresponding linear Poisson structure. Formal and conceptual issues concerning quantum $\kappa$-Poincaré and $\kappa$-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.

Ключевые слова: quantum deformations; quantum groups; Hopf module algebras; covariant quantum spaces; crossed product algebra; twist quantization, quantum Weyl algebra, $\kappa$-Minkowski spacetime; deformed phase space; quantum gravity scale; deformed dispersion relations; time delay

DOI: https://doi.org/10.3842/SIGMA.2010.086

Полный текст: PDF файл (546 kB)
Полный текст: http://emis.mi.ras.ru/journals/SIGMA/2010/086/
Список литературы: PDF файл   HTML файл

Реферативные базы данных:

ArXiv: 1005.4429
Тип публикации: Статья
MSC: 16T05; 17B37; 46L65; 53D55; 81R50; 81R60; 81T75; 83C65
Поступила: 30 марта 2010 г.; в окончательном варианте 10 октября 2010 г.; опубликована 20 октября 2010 г.
Язык публикации: английский

Образец цитирования: Andrzej Borowiec, Anna Pachol, “$\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems”, SIGMA, 6 (2010), 086, 31 pp.

Цитирование в формате AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    Эта публикация цитируется в следующих статьяx:
    1. Lukierski J., “From quantum deformations of relativistic symmetries to modified kinematics and dynamics”, Acta Phys. Polon. B, 41:12 (2010), 2937–2965  mathscinet  zmath  isi  elib
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    3. А. Боровец, А. Пахол, “Дубли Гейзенберга квантованных алгебр Пуанкаре”, ТМФ, 169:2 (2011), 297–306  mathnet  crossref  mathscinet  adsnasa; A. Borowiec, A. Pachol, “Heisenberg doubles of quantized Poincaré algebras”, Theoret. and Math. Phys., 169:2 (2011), 1620–1628  crossref  isi
    4. Meljanac S., Samsarov A., Trampetić J., Wohlgenannt M., “Scalar field propagation in the $\phi^4$ $\kappa$-Minkowski model”, Journal of High Energy Physics, 2011, no. 12, 010  crossref  zmath  isi  scopus
    5. Skoda Z., “Heisenberg double versus deformed derivatives”, Internat. J. Modern Phys. A, 26:27-28 (2011), 4845–4854  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Meljanac S., Krešić-Jurić S., “Differential structure on $\kappa$-Minkowski space, and $\kappa$-Poincaré algebra”, Internat. J. Modern Phys. A, 26:20 (2011), 3385–3402  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. Stjepan Meljanac, Zoran Škoda, Dragutin Svrtan, “Exponential formulas and Lie algebra type star products”, SIGMA, 8 (2012), 013, 15 pp.  mathnet  crossref  mathscinet
    8. Kovacevic D., Meljanac S., “Kappa-Minkowski Spacetime, Kappa-Poincaré Hopf Algebra and Realizations”, Int. J. Geom. Methods Mod. Phys., 9:6 (2012), 1261009  crossref  mathscinet  zmath  isi  elib  scopus
    9. Borowiec A., Lukierski J., Mozrzymas M., Tolstoy V.N., “N=1/2 Deformations of Chiral Superspaces From New Quantum Poincaré and Euclidean Superalgebras”, J. High Energy Phys., 2012, no. 6, 154  crossref  mathscinet  isi  elib  scopus
    10. Lukierski J., Woronowicz M., “Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields”, J. Phys. A-Math. Theor., 45:21 (2012), 215402  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Kovacevic D., Meljanac S., Pachol A., Strajn R., “Generalized Poincaré Algebras, Hopf Algebras and Kappa-Minkowski Spacetime”, Phys. Lett. B, 711:1 (2012), 122–127  crossref  mathscinet  adsnasa  isi  elib  scopus
    12. Meljanac S., Kresic-Juric S., Strajn R., “Differential Algebras on Kappa-Minkowski Space and Action of the Lorentz Algebra”, Int. J. Mod. Phys. A, 27:10 (2012), 1250057  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    13. Kovacevic D., Meljanac S., “Kappa-Minkowski Spacetime, Kappa-Poincaré Hopf Algebra and Realizations”, J. Phys. A-Math. Theor., 45:13 (2012), 135208  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. Borowiec A., Pachol A., “Bicrossproduct Construction Versus Weyl-Heisenberg Algebra”, 7th International Conference on Quantum Theory and Symmetries (Qts7), Journal of Physics Conference Series, 343, IOP Publishing Ltd, 2012, 012090  crossref  isi  scopus
    15. Juric T., Meljanac S., Strajn R., “Differential Forms and Kappa-Minkowski Spacetime From Extended Twist”, Eur. Phys. J. C, 73:7 (2013), 2472  crossref  mathscinet  adsnasa  isi  scopus
    16. Meljanac S., Pachol A., Samsarov A., Gupta K.S., “Different Realizations of Kappa-Momentum”, Phys. Rev. D, 87:12 (2013), 125009  crossref  mathscinet  adsnasa  isi  elib  scopus
    17. Kowalski-Glikman J., “Living in Curved Momentum Space”, Int. J. Mod. Phys. A, 28:12 (2013), 1330014  crossref  mathscinet  adsnasa  isi  scopus
    18. Pachol A., “Short Review on Noncommutative Spacetimes”, 6th International Workshop Dice2012 Spacetime - Matter - Quantum Mechanics: From the Planck Scale to Emergent Phenomena, Journal of Physics Conference Series, 442, eds. Diosi L., Elze H., Fronzoni L., Halliwell J., Prati E., Vitiello G., Yearsley J., IOP Publishing Ltd, 2013  crossref  isi  scopus
    19. Ángel Ballesteros, Francisco J. Herranz, Catherine Meusburger, Pedro Naranjo, “Twisted (2+1) $\kappa$-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes”, SIGMA, 10 (2014), 052, 26 pp.  mathnet  crossref  mathscinet
    20. Borowiec A., Pachol A., “Unified Description for Kappa-Deformations of Orthogonal Groups”, Eur. Phys. J. C, 74:3 (2014), 2812  crossref  mathscinet  adsnasa  isi  scopus
    21. Juric T., Meljanac S., Strajn R., “Twists, Realizations and Hopf Algebroid Structure of Kappa-Deformed Phase Space”, Int. J. Mod. Phys. A, 29:5 (2014), 1450022  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    22. Tajron Jurić, Domagoj Kovačević, Stjepan Meljanac, “$\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting”, SIGMA, 10 (2014), 106, 18 pp.  mathnet  crossref
    23. Andrzej Borowiec, Anna Pachoł, “$\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes”, SIGMA, 10 (2014), 107, 24 pp.  mathnet  crossref
    24. Kovacevic D., Meljanac S., Samsarov A., Skoda Z., “Hermitian Realizations of K-Minkowski Space-Time”, Int. J. Mod. Phys. A, 30:3, SI (2015), 1550019  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    25. Lukierski J., Skoda Z., Woronowicz M., “Kappa-Deformed Covariant Quantum Phase Spaces as Hopf Algebroids”, Phys. Lett. B, 750 (2015), 401–406  crossref  mathscinet  zmath  adsnasa  isi  scopus
    26. Meljanac S., Pachol A., Pikutic D., “Twisted Conformal Algebra Related To Kappa-Minkowski Space”, Phys. Rev. D, 92:10 (2015), 105015  crossref  mathscinet  adsnasa  isi  elib  scopus
    27. Ballesteros A. Herranz F.J. Naranjo P., “Towards (3+1) Gravity Through Drinfel'D Doubles With Cosmological Constant”, Phys. Lett. B, 746 (2015), 37–43  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    28. Pachol A., van Tongeren S.J., “Quantum Deformations of the Flat Space Superstring”, Phys. Rev. D, 93:2 (2016), 026008  crossref  mathscinet  adsnasa  isi  elib  scopus
    29. Arzano M. Nettel F., “Deformed phase spaces with group valued momenta”, Phys. Rev. D, 94:8 (2016), 085004  crossref  mathscinet  isi  scopus
    30. Borowiec A. Pachol A., “Twisted bialgebroids versus bialgebroids from a Drinfeld twist”, J. Phys. A-Math. Theor., 50:5 (2017), 055205  crossref  mathscinet  zmath  isi  scopus
    31. Aschieri P. Borowiec A. Pachol A., “Observables and Dispersion Relations in Kappa-Minkowski Spacetime”, J. High Energy Phys., 2017, no. 10, 152  crossref  mathscinet  zmath  isi  scopus
    32. Mielczarek J., Trzesniewski T., “Spectral Dimension With Deformed Spacetime Signature”, Phys. Rev. D, 96:2 (2017), 024012  crossref  isi  scopus
    33. Stachura P., “On Poisson Structures Related to Kappa-Poincaré Group”, Int. J. Geom. Methods Mod. Phys., 14:9 (2017), 1750133  crossref  mathscinet  zmath  isi  scopus
    34. Lukierski J., Meljanac D., Meljanac S., Pikutic D., Woronowicz M., “Lie-Deformed Quantum Minkowski Spaces From Twists: Hopf-Algebraic Versus Hopf-Algebroid Approach”, Phys. Lett. B, 777 (2018), 1–7  crossref  mathscinet  isi  scopus
    35. Samsarov A., “Could Liv/Noncommutativity Alleviate the Cosmological Constant Problem?”, Int. J. Mod. Phys. D, 27:9 (2018), 1850095  crossref  mathscinet  isi  scopus
    36. Stachura P., “The K-Poincare Group on a C-Level”, Int. J. Math., 30:4 (2019), 1950022  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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