×

zbMATH — the first resource for mathematics

Covariant realizations of kappa-deformed space. (English) Zbl 1189.81114
Summary: We study a Lie algebra type \(\kappa \)-deformed space with an undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. The space deformation depends on an arbitrary vector. Infinitely many covariant realizations in terms of commuting coordinates of undeformed space and their derivatives are constructed. The corresponding coproducts and star products are found and related in a new way. All covariant realizations are physically equivalent. Specially, a few simple realizations are found and discussed. The scalar fields, invariants and the notion of invariant integration is discussed in the natural realization.

MSC:
81R60 Noncommutative geometry in quantum theory
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] S. Doplicher, K. Fredenhagen, J.E. Roberts, Phys. Lett. B 331, 39 (1994) · doi:10.1016/0370-2693(94)90940-7
[2] S. Doplicher, K. Fredenhagen, J.E. Roberts, Commun. Math. Phys. 172, 187 (1995) [hep-th/0303037] · Zbl 0847.53051 · doi:10.1007/BF02104515
[3] N. Seiberg, E. Witten, JHEP 09, 032 (1999) [hep-th/9908142] · Zbl 0957.81085 · doi:10.1088/1126-6708/1999/09/032
[4] J. de Boer, P.A. Grassi, P. van Nieuwenhuizen, Phys. Lett. B 574, 98 (2003) [hep-th/0302078] · Zbl 1058.81076 · doi:10.1016/j.physletb.2003.08.071
[5] M.R. Douglas, N.A. Nekrasov, Rev. Mod. Phys. 73, 977 (2001) [hep-th/0106048] · Zbl 1205.81126 · doi:10.1103/RevModPhys.73.977
[6] R.J. Szabo, Phys. Rep. 378, 207 (2003) [hep-th/0109162] · Zbl 1042.81581 · doi:10.1016/S0370-1573(03)00059-0
[7] R.J. Szabo, Class. Quantum Grav. 23, 199 (2006) [hep-th/0606233] · Zbl 1117.83001 · doi:10.1088/0264-9381/23/22/R01
[8] P. Aschieri, B. Jurco, P. Schupp, J. Wess, Nucl. Phys. B 651, 45 (2003) [hep-th/0205214] · Zbl 1008.81098 · doi:10.1016/S0550-3213(02)00937-9
[9] P. Aschieri, C. Blohmann, M. Dimitrijević, F. Meyer, P. Schupp, J. Wess, Class. Quantum Grav. 22, 3511 (2005) [hep-th/0504183] · Zbl 1129.83011 · doi:10.1088/0264-9381/22/17/011
[10] J. Lukierski, A. Nowicki, H. Ruegg, V.N. Tolstoy, Phys. Lett. B 264, 331 (1991) · doi:10.1016/0370-2693(91)90358-W
[11] J. Lukierski, A. Nowicki, H. Ruegg, Phys. Lett. B 293, 344 (1992) · Zbl 0834.17022 · doi:10.1016/0370-2693(92)90894-A
[12] J. Lukierski, H. Ruegg, Phys. Lett. B 329, 189 (1994) [hep-th/9310117] · doi:10.1016/0370-2693(94)90759-5
[13] S. Majid, H. Ruegg, Phys. Lett. B 334, 348 (1994) [hep-th/9404107] · Zbl 1112.81328 · doi:10.1016/0370-2693(94)90699-8
[14] P. Kosiński, P. Maślanka, hep-th/9411033
[15] A. Sitarz, Phys. Lett. B 349, 42 (1995) [hep-th/9409014] · doi:10.1016/0370-2693(95)00223-8
[16] K. Kosiński, J. Lukierski, P. Maślanka, Phys. Rev. D 62, 025004 (2000) [hep-th/9902037] · doi:10.1103/PhysRevD.62.025004
[17] K. Kosiński, J. Lukierski, P. Maślanka, Czech. J. Phys. 50, 1283 (2000) [hep-th/0009120] · Zbl 1050.81573 · doi:10.1023/A:1022821310096
[18] P. Kosiński, J. Lukierski, P. Maślanka, A. Sitarz, hep-th/0307038
[19] G. Amelino-Camelia, Phys. Lett. 510, 255 (2001) [hep-th/0012238]
[20] G. Amelino-Camelia, Int. J. Mod. Phys. D 11, 35 (2002) [gr-qc/0012051] · Zbl 1062.83500 · doi:10.1142/S0218271802001330
[21] N.R. Bruno, G. Amelino-Camelia, J. Kowalski-Glikman, Phys. Lett. B 522, 133 (2001) [hep-th/0107039] · Zbl 0974.83020 · doi:10.1016/S0370-2693(01)01264-3
[22] J. Kowalski-Glikman, S. Nowak, Phys. Lett. B 539, 126 (2002) [hep- th/0203040] · Zbl 0996.83004 · doi:10.1016/S0370-2693(02)02063-4
[23] G. Amelino-Camelia, M. Arzano, Phys. Rev. D 65, 084044 (2002) [hep-th/0105120] · doi:10.1103/PhysRevD.65.084044
[24] G. Amelino-Camelia, F. D’Andrea, G. Mandanici, JCAP 0309, 006 (2003) [hep-th/0211022]
[25] M. Dimitrijević, L. Jonke, L. Möller, E. Tsouchnika, J. Wess, M. Wohlgenannt, Eur. Phys. J. C 31, 129 (2003) [hep-th/0307149] · Zbl 1032.81529 · doi:10.1140/epjc/s2003-01309-y
[26] M. Dimitrijević, F. Meyer, L. Möller, J. Wess, Eur. Phys. J. C 36, 117 (2004) [hep-th/0310116] · Zbl 1191.81204 · doi:10.1140/epjc/s2004-01887-0
[27] M. Dimitrijević, L. Möller, E. Tsouchnika, J. Phys. A 37, 9749 (2004) [hep-th/0404224] · Zbl 1073.81053 · doi:10.1088/0305-4470/37/41/010
[28] S. Meljanac, M. Stojić, Eur. Phys. J. C 47, 531 (2006) [hep-th/0605133] · Zbl 1191.81138 · doi:10.1140/epjc/s2006-02584-8
[29] L. Möller, JHEP 0512, 029 (2005) [hep-th/0409128] · doi:10.1088/1126-6708/2005/12/029
[30] A. Agostini, G. Amelino-Camelia, M. Arzano, F. D’Andrea, hep-th/0407227
[31] A. Agostini, G. Amelino-Camelia, M. Arzano, A. Marciano, R.A. Tacchi, hep-th/0607221
[32] L. Freidel, J. Kowalski-Glikman, S. Nowak, hep-th/0612170
[33] S. Ghosh, Phys. Lett. B 623, 251 (2005) [hep-th/0506084] · Zbl 1247.83018 · doi:10.1016/j.physletb.2005.07.055
[34] S. Ghosh, P. Pal, Phys. Lett. B 618, 243 (2005) [hep-th/0502192] · Zbl 1247.81225 · doi:10.1016/j.physletb.2005.05.018
[35] S. Ghosh, Phys. Rev. D 74, 084019 (2006) [hep-th/0608206] · doi:10.1103/PhysRevD.74.084019
[36] H.-C. Kim, J.H. Yee, C. Rim, hep-th/0701054
[37] D. Bonatsos, C. Daskaloyannis, Phys. Lett. B 307, 100 (1993) · doi:10.1016/0370-2693(93)90198-Q
[38] S. Meljanac, M. Mileković, S. Pallua, Phys. Lett. B 328, 55 (1994) [hep-th/9404039] · doi:10.1016/0370-2693(94)90427-8
[39] S. Meljanac, M. Mileković, Int. J. Mod. Phys. A 11, 1391 (1996) · Zbl 0985.81556 · doi:10.1142/S0217751X9600064X
[40] S. Meljanac, A. Perica, J. Phys. A Math. Gen. 27, 4737 (1994) · doi:10.1088/0305-4470/27/14/004
[41] S. Meljanac, A. Perica, Mod. Phys. Lett. A 9, 3293 (1994) [hep-th/9409180] · Zbl 1021.81594 · doi:10.1142/S0217732394003117
[42] S. Meljanac, A. Perica, D. Svrtan, J. Phys. A 36, 6337 (2003) [math-ph/0304038] · Zbl 1027.82004 · doi:10.1088/0305-4470/36/23/305
[43] S. Meljanac, D. Svrtan, math-ph/0304040
[44] S. Meljanac, D. Svrtan, Math. Commun. 1, 1 (1996) [math-ph/0304039]
[45] V. Bardek, S. Meljanac, Eur. Phys. J. C 17, 539 (2000) [hep-th/0009099] · Zbl 1099.81510 · doi:10.1007/s100520000457
[46] V. Bardek, L. Jonke, S. Meljanac, M. Mileković, Phys. Lett. B 531, 311 (2002) [hep-th/0107053] · Zbl 1039.81529 · doi:10.1016/S0370-2693(02)01481-8
[47] S. Meljanac, M. Mileković, M. Stojić, Eur. Phys. J. C 24, 331 (2002) [math-ph/0201061] · Zbl 1099.81511 · doi:10.1007/s100520200914
[48] L. Jonke, S. Meljanac, Phys. Lett. B 526, 149 (2002) [hep-th/0106135] · Zbl 0983.81030 · doi:10.1016/S0370-2693(01)01464-2
[49] V.P. Nair, A.P. Polychronakos, Phys. Lett. B 505, 267 (2001) [hep-th/0011172] · Zbl 0977.81046 · doi:10.1016/S0370-2693(01)00339-2
[50] L. Jonke, S. Meljanac, Eur. Phys. J. C 29, 433 (2003) [hep-th/0210042] · Zbl 1099.81515 · doi:10.1140/epjc/s2003-01205-6
[51] I. Dadić, L. Jonke, S. Meljanac, Acta Phys. Slovaca 55, 149 (2005) [hep-th/0301066]
[52] A. Kempf, G. Mangano, R.B. Mann, Phys. Rev. D 52, 1108 (1995) [hep-th/9412167] · doi:10.1103/PhysRevD.52.1108
[53] L.N. Chang, D. Minic, N. Okamura, T. Takeuchi, Phys. Rev. D 65, 125027 (2002) [hep-th/0201017] · doi:10.1103/PhysRevD.65.125027
[54] I. Dadić, L. Jonke, S. Meljanac, Phys. Rev. D 67, 087701 (2003) [hep-th/0210264] · doi:10.1103/PhysRevD.67.087701
[55] J. Wess, Deformed coordinates spaces, Derivatives, Lecture given at the Balkan workshop BW2003, August 2003, Vrnjačka Banja, Serbia, [hep-th/0408080]
[56] M. Chaichian, P.P. Kulish, K. Nishijima, A. Tureanu, Phys. Lett. B 604, 98 (2004) [hep-th/0408069] · Zbl 1247.81518 · doi:10.1016/j.physletb.2004.10.045
[57] M. Chaichian, P. Presnajder, A. Tureanu, Phys. Rev. Lett. 94, 151602 (2005) [hep-th/0409096] · doi:10.1103/PhysRevLett.94.151602
[58] J. Lukierski, M. Woronowicz, Phys. Lett. B 633, 116 (2006) [hep-th/0508083] · Zbl 1247.81216 · doi:10.1016/j.physletb.2005.11.052
[59] N. Durov, S. Meljanac, A. Samsarov, Z. Škoda, J. Algebra 309 (2007) [math.RT/0604096] · Zbl 1173.17014
[60] V. Kathotia, Int. J. Math. Math. Sci. 11, 523 (2000) [math.qa/9811174]
[61] L. Freidel, E.R. Livine, Class. Quantum Grav. 23, 2021 (2006) [hep-th/0502106] · Zbl 1091.83503 · doi:10.1088/0264-9381/23/6/012
[62] L. Freidel, E.R. Livine, Phys. Rev. Lett. 96, 221301 (2006) [hep-th/0512113] · Zbl 1228.83047 · doi:10.1103/PhysRevLett.96.221301
[63] S. Majid, J. Math. Phys. 46, 103520 (2005) [hep-th/0507271] · Zbl 1111.81099 · doi:10.1063/1.2084748
[64] L. Freidel, S. Majid, hep/th-0601004
[65] R. Banerjee, S. Kulkarni, S. Samatra, JHEP 0605, 077 (2006) [hep-th/0602151] · doi:10.1088/1126-6708/2006/05/077
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.