On κ-deformation and triangular quasibialgebra structure

Nuclear Physics B

Volumn 809, Issue 3, 2009, Pages 439-451

  Young, C A S ^a   Zegers, R ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 57649104888     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2008.09.025     Document Type: Article

References (59)

1. Lukierski J., Nowicki A., and Ruegg H. New quantum Poincaré algebra and k-deformed field theory. Phys. Lett. B 293 (1992) 344
2. Lukierski J., and Ruegg H. Quantum kappa Poincaré in any dimension. Phys. Lett. B 329 (1994) 189. hep-th/9310117
3. Majid S., and Ruegg H. Bicrossproduct structure of kappa Poincaré group and noncommutative geometry. Phys. Lett. B 334 (1994) 348. hep-th/9405107
4. Lukierski J. Quantum deformations of Einstein's relativistic symmetries. AIP Conf. Proc. 861 (2006) 398. hep-th/0604083
5. Lukierski J., and Nowicki A. Doubly special relativity versus κ-deformation of relativistic kinematics. Int. J. Mod. Phys. A 18 (2003) 7. hep-th/0203065
6. Young C.A.S., and Zegers R. Covariant particle statistics and intertwiners of the kappa-deformed Poincaré algebra. Nucl. Phys. B 797 (2008) 537. arXiv: 0711.2206 [hep-th]
7. Young C.A.S., and Zegers R. Covariant particle exchange for κ-deformed theories in 1 + 1 dimensions. Nucl. Phys. B 804 (2008) 342-360. arXiv: 0803.2659 [hep-th]
8. Daszkiewicz M., Lukierski J., and Woronowicz M. κ-Deformed statistics and classical fourmomentum addition law. hep-th/0703200
9. Dimitrijevic M., Jonke L., Moller L., Tsouchnika E., Wess J., and Wohlgenannt M. Field theory on kappa-spacetime. Czech. J. Phys. 54 (2004) 1243. hep-th/0407187
10. Dimitrijevic M., Jonke L., Moller L., Tsouchnika E., Wess J., and Wohlgenannt M. Deformed field theory on kappa-spacetime. Eur. Phys. J. C 31 (2003) 129. hep-th/0307149
11. Daszkiewicz M., Imilkowska K., Kowalski-Glikman J., and Nowak S. Scalar field theory on kappa-Minkowski space-time and doubly special relativity. Int. J. Mod. Phys. A 20 (2005) 4925. hep-th/0410058
12. Agostini A., Amelino-Camelia G., Arzano M., and D'Andrea F. A cyclic integral on kappa-Minkowski noncommutative space-time. Int. J. Mod. Phys. A 21 (2006) 3133
13. Agostini A., Amelino-Camelia G., Arzano M., Marciano A., and Tacchi R.A. Generalizing the Noether theorem for Hopf-algebra spacetime symmetries. Mod. Phys. Lett. A 22 (2007) 1779. hep-th/0607221
14. Agostini A., Amelino-Camelia G., Arzano M., and D'Andrea F. Action functional for kappa-Minkowski noncommutative spacetime. hep-th/0407227
15. Agostini A., Amelino-Camelia G., and D'Andrea F. Hopf-algebra description of noncommutative-spacetime symmetries. Int. J. Mod. Phys. A 19 (2004) 5187. hep-th/0306013
16. Freidel L., Kowalski-Glikman J., and Nowak S. Field theory on κ-Minkowski space revisited: Noether charges and breaking of Lorentz symmetry. arXiv: 0706.3658 [hep-th]
17. Lukierski J., Ruegg H., and Zakrzewski W.J. Classical quantum mechanics of free kappa relativistic systems. Ann. Phys. 243 (1995) 90. hep-th/9312153
18. Kosinski P., Lukierski J., and Maslanka P. Local D = 4 field theory on kappa-deformed Minkowski space. Phys. Rev. D 62 (2000) 025004. hep-th/9902037
19. Grosse H., and Wohlgenannt M. On kappa-deformation and UV/IR mixing. Nucl. Phys. B 748 (2006) 473. hep-th/0507030
20. Kim H.C., Rim C., and Yee J.H. Symmetric ordering effect on Casimir energy in κ-Minkowski spacetime. arXiv: 0803.2333 [hep-th]
21. Kim H.C., Rim C., and Yee J.H. Casimir energy of a spherical shell in κ-Minkowski spacetime. arXiv: 0710.5633 [hep-th]
22. Amelino-Camelia G., and Arzano M. Coproduct and star product in field theories on Lie-algebra non-commutative space-times. Phys. Rev. D 65 (2002) 084044. hep-th/0105120
23. Frappat L., and Sciarrino A. Lattice space-time from Poincaré and kappa Poincaré algebras. Phys. Lett. B 347 (1995) 28
24. Moller L. A symmetry invariant integral on kappa-deformed spacetime. JHEP 0512 (2005) 029. hep-th/0409128
25. Kosinski P., Maslanka P., Lukierski J., and Sitarz A. Towards kappa-deformed D = 4 relativistic field theory. Czech. J. Phys. 48 (1998) 1407
26. Meljanac S., and Stojic M. New realizations of Lie algebra kappa-deformed Euclidean space. Eur. Phys. J. C 47 (2006) 531. hep-th/0605133
27. Kresic-Juric S., Meljanac S., and Stojic M. Covariant realizations of kappa-deformed space. Eur. Phys. J. C 51 (2007) 229. hep-th/0702215
28. Dimitrijevic M., Moller L., and Tsouchnika E. Derivatives, forms and vector fields on the kappa-deformed Euclidean space. J. Phys. A 37 (2004) 9749. hep-th/0404224
29. Govindarajan T.R., Gupta K.S., Harikumar E., Meljanac S., and Meljanac D. Twisted statistics in kappa-Minkowski spacetime. Phys. Rev. D 77 (2008) 105010. arXiv: 0802.1576 [hep-th]
30. Meljanac S., Samsarov A., Stojic M., and Gupta K.S. Kappa-Minkowski space-time and the star product realizations. Eur. Phys. J. C 53 (2008) 295. arXiv: 0705.2471 [hep-th]
31. Weinberg S. The Quantum Theory of Fields. Vol. 1: Foundations (1995), Cambridge Univ. Press, Cambridge
32. Kosinski P., Lukierski J., Maslanka P., and Sobczyk J. The Classical basis for kappa-deformed Poincaré (super)algebra and the second kappa-deformed supersymmetric Casimir. Mod. Phys. Lett. A 10 (1995) 2599. hep-th/9412114
33. Giller S., Gonera C., and Majewski M. Deformation map for generalized κ-Poincaré and κ-Weyl algebras. Acta Phys. Pol. B 27 (1996) 2131
34. Kosinski P., Lukierski J., and Maslanka P. Kappa-deformed Wigner construction of relativistic wave functions and free fields on kappa-Minkowski space. Nucl. Phys. B (Proc. Suppl.) 102 (2001) 161. hep-th/0103127
35. Majid S. Foundations of Quantum Group Theory (1995), Cambridge Univ. Press, Cambridge
36. Arzano M. Quantum fields, Noether charges and kappa-spacetime symmetries. arXiv: 0711.3222 [hep-th]
37. Arzano M. Quantum fields, non-locality and quantum group symmetries. Phys. Rev. D 77 (2008) 025013. arXiv: 0710.1083 [hep-th]
38. Arzano M., and Marciano A. Fock space, quantum fields and kappa-Poincaré symmetries. Phys. Rev. D 76 (2007) 125005. arXiv: 0707.1329 [hep-th]
39. Daszkiewicz M., Lukierski J., and Woronowicz M. Towards quantum noncommutative κ-deformed field theory. Phys. Rev. D 77 (2008) 105007. arXiv: 0708.1561 [hep-th]
40. Daszkiewicz M., Lukierski J., and Woronowicz M. Quantization of kappa-deformed free fields and kappa-deformed oscillators. arXiv: 0712.0350 [hep-th]
41. Daszkiewicz M., Lukierski J., and Woronowicz M. Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields. arXiv: 0807.1992 [hep-th]
42. Zakrzewski S. Quantum Poincaré group related to the kappa-Poincaré algebra. J. Phys. A: Math. Gen. 27 (1994) 2075-2082
43. Herranz F.J., and Santander M. (Anti)de Sitter/Poincaré symmetries and representations from Poincaré/Galilei through a classical deformation approach. J. Phys. A 41 (2008) 015204. math-ph/0612059
44. Zakrzewski S. Poisson Poincaré groups. hep-th/9412099
45. Daszkiewicz M. Canonical, Lie-algebraic and quadratic twist deformations of Galilei group. arXiv: 0807.0133 [hep-th]
46. Meusburger C., and Schroers B.J. Generalised Chern-Simons actions for 3d gravity and kappa-Poincaré symmetry. arXiv: 0805.3318 [gr-qc]
47. Celeghini E., Giachetti R., Sorace E., and Tarlini M. The three-dimensional Euclidean quantum group E (3) q and its R-matrix. J. Math. Phys. 32 (1991) 1159
48. Vermaseren J.A.M. New features of FORM. math-ph/0010025
49. Drinfel'd V.G. On the structure of quasitriangular quasi-Hopf algebras. Funktsional. Anal. i Prilozhen. 26 1 (1992) 78-80 translation in:
50. Drinfel'd V.G. On the structure of quasitriangular quasi-Hopf algebras. Funct. Anal. Appl. 26 1 (1992) 63-65
51. Drinfel'd V.G. Quasi-Hopf algebras. Algebra i Analiz 1 6 (1989) 114-148 translation in:
52. Drinfel'd V.G. Quasi-Hopf algebras. Leningrad Math. J. 1 6 (1990) 1419-1457
53. Mack G., and Schomerus V. Quasi-Hopf quantum symmetry in quantum theory. Nucl. Phys. B 370 (1992) 185
54. Kowalski-Glikman J., and Starodubtsev A. Can we see gravitational collapse in (quantum) gravity perturbation theory?. gr-qc/0612093
55. Amelino-Camelia G., Smolin L., and Starodubtsev A. Quantum symmetry, the cosmological constant and Planck scale phenomenology. Class. Quantum Grav. 21 (2004) 3095. hep-th/0306134
56. Freidel L., Kowalski-Glikman J., and Smolin L. 2 + 1 gravity and doubly special relativity. Phys. Rev. D 69 (2004) 044001. hep-th/0307085
57. Goldin G.A., and Majid S. On the Fock space for nonrelativistic anyon fields and braided tensor products. J. Math. Phys. 45 (2004) 3770-3787
58. Beggs E.J., and Majid S. Quantization by cochain twists and nonassociative differentials. math.QA/0506450
59. Freidel L., and Kowalski-Glikman J. κ-Minkowski space, scalar field, and the issue of Lorentz invariance. arXiv: 0710.2886 [hep-th]