Star product and invariant integration for Lie Type noncommutative spacetimes

Journal of High Energy Physics

Volumn 2007, Issue 8, 2007, Pages

  Chryssomalakos, Chryssomalis ^a   Okon, Elias ^b  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

Non commutative geometry; Space time symmetries

Indexed keywords

EID: 77953255791     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2007/08/012     Document Type: Article

References (34)

1. M. Dimitrijevic et al., Deformed field theory on kappa-spacetime, Eur. Phys. J. C 31 (2003) 129 [hep-th/0307149].
2. M. Dimitrijevic, F. Meyer, L. Moller and J. Wess, Gauge theories on the kappa-Minkowski spacetime, Eur. Phys. J. C 36 (2004) 117 [hep-th/0310116].
3. J. Madore, S. Schraml, P. Schupp and J. Wess, Gauge theory on noncommutative spaces, Eur. Phys. J. C 16 (2000) 161 [hep-th/0001203].
4. P. Kosinski, J. Lukierski and P. Maslanka, Local field theory on kappa-Minkowski space, star products and noncommutative translations, Czech. J. Phys. 50 (2000) 1283 [hep-th/0009120].
5. P. Aschieri, M. Dimitrijevic, F. Meyer, S. Schraml and J. Wess, Twisted gauge theories, Lett. Math. Phys. 78 (2006) 61 [hep-th/0603024].
6. R.J. Szabo, Quantum field theory on noncommutative spaces, Phys. Rept. 378 (2003) 207 [hep-th/0109162].
7. A.H. Fatollahi and M. Khorrami, Field theories on spaces with linear fuzziness, hep-th/0612013.
8. M. Daszkiewicz, J. Lukierski and M. Woronowicz, Noncommutative translations and *-product formalism, hep-th/0701152.
9. L. Moller, A symmetry invariant integral on kappa-deformed spacetime, JHEP 12 (2005) 029 [hep-th/0409128].
10. λand the fuzzy sphere, Phys. Rev. D 66 (2002) 025025 [hep-th/0110291].
11. C.K. Zachos, Geometrical evaluation of star products, J. Math. Phys. 41 (2000) 5129 [hep-th/9912238].
12. P. Maslanka, Noncommutative parameters of quantum symmetries and star products, Phys. Atom. Nucl. 64 (2001) 2139 [hep-th/0012056].
13. J.M. Gracia-Bondia, F. Lizzi, G. Marmo and P. Vitale, Infinitely many star products to play with, JHEP 04 (2002) 026 [hep-th/0112092].
14. A. Sykora, The application of *-products to noncommutative geometry and gauge theory, hep-th/0412012.
15. A.C. Hirshfeld and P. Henselder, Star products and perturbative quantum field theory, Ann. Phys. (NY) 298 (2002) 382 [hep-th/0208194].
16. J. Wess, Differential calculus and gauge transformations on a deformed space, hep-th/0607251.
17. A. Sitarz, Noncommutative differential calculus on the kappa Minkowski space, Phys. Lett. B 349 (1995) 42 [hep-th/9409014].
18. S. Majid and H. Ruegg, Bicrossproduct structure of kappa Poincaré group and noncommutative geometry, Phys. Lett. B 334 (1994) 348 [hep-th/9405107].
19. S. Gutt, An explicit *-product on the cotangent bundle of a Lie group, Lett. Math. Phys. 7 (1983) 249.
20. M. Bordemann, N. Neumaier and S. Waldmann, Homogeneous Fedosov star products on cotangent bundles I: Weyl and standard ordering with differential operator representation, Commun. Math. Phys. 198 (1998) 363.
21. M. Kontsevich, Deformation quantization of Poisson manifolds, I, Lett. Math. Phys. 66 (2003) 157 [q-alg/9709040].
22. G. Dito, Kontsevich star product on the dual of a Lie algebra, Lett. Math. Phys. 48 (1999) 307
23. V. Kathotia, Kontsevich's universal formula for deformation quantization and the Campbell-Baker-Hausdorff formula, I, (1998).
24. P. Bieliavsky, M. Bordemann, S. Gutt and S. Waldmann, Traces for star products on the dual of a Lie algebra, Rev. Math. Phys. 15 (2003) 425.
25. G. Felder and B. Shoikhet, Deformation quantization with traces, Lett. Math. Phys. 53 (2000) 75.
26. H. Basart, M. Flato, A. Lichnerowicz and D. Sternheimer, Deformation theory applied to quantization and statistical mechanics, Lett. Math. Phys. 8 (1984) 483.
27. H. Basart and A. Lichnerowicz, Conformal symplectic geometry, deformations, rigidity and geometrical (KMS) conditions, Lett. Math. Phys. 10 (1985) 167.
28. M. Bordemann, H. Römer and S. Waldmann, A remark on formal KMS states in deformation quantization, Lett. Math. Phys. 45 (1998) 49.
29. A. Weinstein, The modular automorphism group of a Poisson manifold, J. Geom. Phys. 23 (1997) 379.
30. C. Chryssomalakos and A. Turbiner, Canonical commutation relation preserving maps, J. Phys. A 34 (2001) 10475.
31. S. Meljanac, A. Samsarov, M. Stojic and K. S. Gupta, Kappa-Minkowski space-time and the star product realizations, (2007).
32. S. Meljanac and M. Stojic, New realizations of Lie algebra kappa-deformed euclidean space, Eur. Phys. J. C 47 (2006) 531 [hep-th/0605133].
33. S. Kurkcuoglu and C. Saemann, Drinfeld twist and general relativity with fuzzy spaces, Class, and Quant. Grav. 24 (2007) 291.
34. S. Majid, Foundations of Quantum Group Theory, Cambridge University Press (1995).