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

被引：53

作者：

Borowiec, Andrzej ^{[1
]}

Pachol, Anna ^{[1
]}

机构：

[1] Univ Wroclaw, Inst Theoret Phys, PL-50204 Wroclaw, Poland

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2010年 / 6卷

关键词：

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; DOUBLY-SPECIAL RELATIVITY; DEFORMATION QUANTIZATION; QUANTUM DEFORMATIONS; CROSSED-PRODUCTS; D=4 LORENTZ; PROPER-TIME; NONCOMMUTATIVE GEOMETRY; TWIST QUANTIZATION; DEFORMED SPACETIME; POISSON STRUCTURES;

D O I：

10.3842/SIGMA.2010.086

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Poincare 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 (Stuckelberg 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-Poincare 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.

引用

页数：31

共 162 条

[1] A limit on the variation of the speed of light arising from quantum gravity effects [J].

Abdo, A. A. ;

Ackermann, M. ;

Ajello, M. ;

Asano, K. ;

Atwood, W. B. ;

Axelsson, M. ;

Baldini, L. ;

Ballet, J. ;

Barbiellini, G. ;

Baring, M. G. ;

Bastieri, D. ;

Bechtol, K. ;

Bellazzini, R. ;

Berenji, B. ;

Bhat, P. N. ;

Bissaldi, E. ;

Bloom, E. D. ;

Bonamente, E. ;

Bonnell, J. ;

Borgland, A. W. ;

Bouvier, A. ;

Bregeon, J. ;

Brez, A. ;

Briggs, M. S. ;

Brigida, M. ;

Bruel, P. ;

Burgess, J. M. ;

Burnett, T. H. ;

Caliandro, G. A. ;

Cameron, R. A. ;

Caraveo, P. A. ;

Casandjian, J. M. ;

Cecchi, C. ;

Celik, Oe ;

Chaplin, V. ;

Charles, E. ;

Cheung, C. C. ;

Chiang, J. ;

Ciprini, S. ;

Claus, R. ;

Cohen-Tanugi, J. ;

Cominsky, L. R. ;

Connaughton, V. ;

Conrad, J. ;

Cutini, S. ;

Dermer, C. D. ;

de Angelis, A. ;

de Palma, F. ;

Digel, S. W. ;

Dingus, B. L. .

NATURE, 2009, 462 (7271) :331-334

[2] Fermi Observations of High-Energy Gamma-Ray Emission from GRB 080916C [J].

Abdo, A. A. ;

Ackermann, M. ;

Arimoto, M. ;

Asano, K. ;

Atwood, W. B. ;

Axelsson, M. ;

Baldini, L. ;

Ballet, J. ;

Band, D. L. ;

Barbiellini, G. ;

Baring, M. G. ;

Bastieri, D. ;

Battelino, M. ;

Baughman, B. M. ;

Bechtol, K. ;

Bellardi, F. ;

Bellazzini, R. ;

Berenji, B. ;

Bhat, P. N. ;

Bissaldi, E. ;

Blandford, R. D. ;

Bloom, E. D. ;

Bogaert, G. ;

Bogart, J. R. ;

Bonamente, E. ;

Bonnell, J. ;

Borgland, A. W. ;

Bouvier, A. ;

Bregeon, J. ;

Brez, A. ;

Briggs, M. S. ;

Brigida, M. ;

Bruel, P. ;

Burnett, T. H. ;

Burrows, D. ;

Busetto, G. ;

Caliandro, G. A. ;

Cameron, R. A. ;

Caraveo, P. A. ;

Casandjian, J. M. ;

Ceccanti, M. ;

Cecchi, C. ;

Celotti, A. ;

Charles, E. ;

Chekhtman, A. ;

Cheung, C. C. ;

Chiang, J. ;

Ciprini, S. ;

Claus, R. ;

Cohen-Tanugi, J. .

SCIENCE, 2009, 323 (5922) :1688-1693

[3] NEW DYNAMICAL GROUP FOR RELATIVISTIC QUANTUM MECHANICS OF ELEMENTARY PARTICLES [J].

AGHASSI, JJ ;

ROMAN, P ;

SANTILLI, RM .

PHYSICAL REVIEW D, 1970, 1 (10) :2753-&

[4] Limits on an Energy Dependence of the Speed of Light from a Flare of the Active Galaxy PKS 2155-304 [J].

Aharonian, F. ;

Akhperjanian, A. G. ;

de Almeida, U. Barres ;

Bazer-Bachi, A. R. ;

Becherini, Y. ;

Behera, B. ;

Beilicke, M. ;

Benbow, W. ;

Bernloehr, K. ;

Boisson, C. ;

Bochow, A. ;

Borrel, V. ;

Braun, I. ;

Brion, E. ;

Brucker, J. ;

Brun, P. ;

Buehler, R. ;

Bulik, T. ;

Buesching, I. ;

Boutelier, T. ;

Carrigan, S. ;

Chadwick, P. M. ;

Charbonnier, A. ;

Chaves, R. C. G. ;

Chounet, L. -M. ;

Clapson, A. C. ;

Coignet, G. ;

Costamante, L. ;

Dalton, M. ;

Degrange, B. ;

Deil, C. ;

Dickinson, H. J. ;

Djannati-Atai, A. ;

Domainko, W. ;

Drury, L. O'C. ;

Dubois, F. ;

Dubus, G. ;

Dyks, J. ;

Egberts, K. ;

Emmanoulopoulos, D. ;

Espigat, P. ;

Farnier, C. ;

Feinstein, F. ;

Fiasson, A. ;

Foerster, A. ;

Fontaine, G. ;

Fuessling, M. ;

Gabici, S. ;

Gallant, Y. A. ;

Gerard, L. .

PHYSICAL REVIEW LETTERS, 2008, 101 (17)

[5] Possible polarization and spin-dependent aspects of quantum gravity [J].

Ahluwalia, D. V. ;

Gresnigt, N. G. ;

Nielsen, Alex B. ;

Schritt, D. ;

Watson, T. F. .

INTERNATIONAL JOURNAL OF MODERN PHYSICS D, 2008, 17 (3-4) :495-504

[6] A freely falling frame at the interface of gravitational and quantum realms [J].

Ahluwalia-Khalilova, DV .

CLASSICAL AND QUANTUM GRAVITY, 2005, 22 (07) :1433-1450

[7] Noncommutative geometry of super-Jordanian OSph(2/1) covariant quantum space [J].

Aizawa, N ;

Chakrabarti, R .

JOURNAL OF MATHEMATICAL PHYSICS, 2004, 45 (04) :1623-1638

[8] Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope [J].

Albert, J. ;

Aliu, E. ;

Anderhub, H. ;

Antonelli, L. A. ;

Antoranz, P. ;

Backes, M. ;

Baixeras, C. ;

Barrio, J. A. ;

Bartko, H. ;

Bastieri, D. ;

Becker, J. K. ;

Bednarek, W. ;

Berger, K. ;

Bernardini, E. ;

Bigongiari, C. ;

Biland, A. ;

Bock, R. K. ;

Bonnoli, G. ;

Bordas, P. ;

Bosch-Ramon, V. ;

Bretz, T. ;

Britvitch, I. ;

Camara, M. ;

Carmona, E. ;

Chilingarian, A. ;

Commichau, S. ;

Contreras, J. L. ;

Cortina, J. ;

Costado, M. T. ;

Covino, S. ;

Curtef, V. ;

Dazzi, F. ;

De Angelis, A. ;

De Cea del Pozo, E. ;

Mendez, C. Delgado ;

de los Reyes, R. ;

De Lotto, B. ;

De Maria, M. ;

De Sabata, F. ;

Dominguez, A. ;

Dorner, D. ;

Doro, M. ;

Errando, M. ;

Fagiolini, M. ;

Ferenc, D. ;

Fernandez, E. ;

Firpo, R. ;

Fonseca, M. V. ;

Font, L. ;

Galante, N. .

PHYSICS LETTERS B, 2008, 668 (04) :253-257

[9] Doubly-special relativity: First results and key open problems [J].

Amelino-Camelia, G .

INTERNATIONAL JOURNAL OF MODERN PHYSICS D, 2002, 11 (10) :1643-1669

[10] Testable scenario for relativity with minimum length [J].

Amelino-Camelia, G .

PHYSICS LETTERS B, 2001, 510 (1-4) :255-263

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