A gravity theory on noncommutative spaces

Classical and Quantum Gravity

Volumn 22, Issue 17, 2005, Pages 3511-3532

  Aschieri, Paolo ^a   Blohmann, Christian ^b,c   Dimitrijević, Marija ^d,e,f   Meyer, Frank ^d,e   Schupp, Peter ^b   Wess, Julius ^d,e  

^a INFN SEZIONE DI ROMA   (Italy)

^b JACOBS UNIVERSITY BREMEN   (Germany)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d UNIVERSITY OF MUNICH   (Germany)

^e MAX PLANCK INSTITUT FÜR PHYSIK   (Germany)

^f UNIVERSITY OF BELGRADE   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 24144475305     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/22/17/011     Document Type: Article

References (55)

1. Wheeler J A 1962 Geometrodynamics (New York: Academic)
2. Witten L 1962 Gravitation: An Introduction to Current Research (New York: Wiley)
3. Heisenberg W 1985 Letter from Heisenberg to Peierls vol 2 W Pauli, Scientific Correspondence (Berlin: Springer)
4. Snyder H S 1947 Quantized space-time Phys. Rev. 71 38
5. Manin Y I 1989 Multiparametric quantum deformation of the general linear supergroup Commun. Math. Phys. 123 163
6. Wess J 2000 q-Deformed Heisenberg Algebras (Lecture Notes in Physics vol 543) (Berlin: Springer) (Preprint math.ph/9910013)
7. Behr W et al 2003 The Z to gamma gamma, gg decays in the noncommutative standard model Eur. Phys. J. C 29 441 (Preprint hep-ph/0202121)
8. Ohl T and Reuter J 2004 Testing the noncommutative standard model at a future photon collider Phys. Rev. D 70 076007 (Preprint hep-ph/0406098)
9. Melić B, Passek-Kumerički K, Trampetić J, Schupp P and Wohlgenannt M 2005 The standard model on non-commutative space-time: strong interactions included Preprint hep-ph/0503064
10. Martin C P and Tamarit C 2005 The U(1)A anomaly in noncommutative SU(N) theories Preprint hep-th/0503139
11. Grosse H and Liao Y 2001 Pair production of neutral Higgs bosons through noncommutative QED interactions at linear colliders Phys. Rev. D 64 115007 (Preprint hep-ph/0105090)
12. Madore J, Schraml S, Schupp P and Wess J 2000 Gauge theory on noncommutative spaces Eur. Phys. J. C 16 161 (Preprint hep-th/0001203)
13. Wess J 2005 Gauge Theory on Noncommutative Algebras and the Seiberg-Witten Transformations (Lecture Notes in Physics vol 662) (Berlin: Springer)
14. Bayen F, Flato M, Fronsdal C, Lichnerowicz A and Sternheimer D 1978 Deformation theory and quantization Ann. Phys. 111 61
15. Gayral V, Gracia-Bondia J M and Ruiz Ruiz F 2005 Position-dependent noncommutative products: classical construction and field theory Preprint hep-th/0504022
16. Jambor C and Sykora A 2004 Realization of algebras with the help of *-products Preprint hep-th/0405268
17. Seiberg N and Witten E 1999 String theory and noncommutative geometry J. High Energy Phys. JHEP09(1999)032 (Preprint hep-th/9908142)
18. Jurčo B, Schraml S, Schupp P and Wess J 2000 Enveloping algebra valued gauge transformations for non-Abelian gauge groups on non-commutative spaces Eur. Phys. J. C 17 521 (Preprint hep-th/0006246)
19. Jurčo B, Möller L, Schraml S, Schupp P and Wess J 2001 Construction of non-Abelian gauge theories on noncommutative spaces Eur. Phys. J. C 21 383 (Preprint hep-th/0104153)
20. Jurčo B, Schupp P and Wess J 2001 Nonabelian noncommutative gauge theory via noncommutative extra dimensions Nucl. Phys. B 604 148 (Preprint hep-th/0102129)
21. q(2)-covariant plane Int. J. Mod. Phys. A 19 3349 (Preprint hep-th/0309053)
22. Dimitrijević M, Meyer F, Möller L and Wess J 2004 Gauge theories on the kappa-Minkowski spacetime Eur. Phys. J. C 36 117 (Preprint hep-th/0310116)
23. Behr W and Sykora A 2004 Construction of gauge theories on curved noncommutative spacetime Nucl. Phys. B 698 473 (Preprint hep-th/0309145)
24. Schupp P 2001 Non-Abelian gauge theory on noncommutative spaces Talk given at HEP2001 (Budapest, Hungary) (Preprint hep-th/0111038)
25. Chamseddine A H, Felder G and Fröhlich J 1993 Gravity in noncommutative geometry Commun. Math. Phys. 155 205 (Preprint hep-th/9209044)
26. Madore J 1992 Gravity on fuzzy space-time Class. Quantum Grav. 9 69
27. Castellani L 1995 Differential calculus on ISO-q(N), quantum Poincaré algebra and q gravity Commun. Math. Phys. 171 383 (Preprint hep-th/9312179)
28. Castellani L 1994 The Lagrangian of q Poincaré gravity Phys. Lett. B 327 22 (Preprint hep-th/9402033)
29. Madore J and Mourad J 1998 Quantum space-time and classical gravity J. Math. Phys. 39 423 (Preprint gr-qc/9607060)
30. Connes A 1996 Gravity coupled with matter and the foundation of non-commutative geometry Commun. Math. Phys. 182 155 (Preprint hep-th/9603053)
31. Chamseddine A H 2001 Deforming Einstein's gravity Phys. Lett. B 504 33 (Preprint hep-th/0009153)
32. Moffat J W 2000 Noncommutative quantum gravity Phys. Lett. B 491 345 (Preprint hep-th/0007181)
33. Vacaru S I 2001 Gauge and Einstein gravity from non-Abelian gauge models on noncommutative spaces Phys. Lett. B 498 74 (Preprint hep-th/0009163)
34. Cardella M A and Zanon D 2003 Noncommutative deformation of four dimensional Einstein gravity Class. Quantum Grav. 20 L95 (Preprint hep-th/0212071)
35. Cacciatori S, Klemm D, Martucci L and Zanon D 2002 Noncommutative Einstein-AdS gravity in three dimensions Phys. Lett. B 536 101 (Preprint hep-th/0201103)
36. Cacciatori S et al 2002 Noncommutative gravity in two dimensions Class. Quantum Grav. 19 4029 (Preprint hep-th/0203038)
37. Ardalan F, Arfaei H, Garousi M R and Ghodsi A 2003 Gravity on noncommutative D-branes Int. J. Mod. Phys. A 18 1051 (Preprint hep-th/0204117)
38. Garcia-Compean H, Obregon O, Ramirez C and Sabido M 2003 Noncommutative topological theories of gravity Phys. Rev. D 68 045010
39. Garcia-Compean H, Obregon O, Ramirez C and Sabido M 2003 Noncommutative self-dual gravity Phys. Rev. D 68 044015
40. Chu C-S and Ho P-M 1999 Noncommutative open string and D-brane Nucl. Phys. B 550 151 (Preprint hep-th/9812219)
41. Schomerus V 1999 D-branes and deformation quantization J. High Energy Phys. JHEP06(1999)030 (Preprint hep-th/9903205)
42. Moyal J E 1949 Quantum mechanics as a statistical theory Proc. Camb. Phil. Soc. 45 99
43. Waldmann S 1999 Zur Deformationsquantisierung in der klassischen Mechanik: Observablen, Zustände und Darstellungen PhD Thesis
44. Woronowicz S L 1989 Differential calculus on compact matrix pseudogroups (quantum groups) Commun. Math. Phys. 122 125
45. Wess J and Zumino B 1991 Covariant differential calculus on the quantum hyperplane Nucl. Phys. B 18 302
46. Abe E 1980 Hopf Algebras (Cambridge: Cambridge University Press)
47. Chari V and Pressley A 1995 A Guide to Quantum Groups (Cambridge: Cambridge University Press) p 651
48. Klimyk A and Schmüdgen K 1997 Quantum Groups and Their Representations (Berlin: Springer) p 552
49. Dimitrijević M and Wess J 2004 Deformed bialgebra of diffeomorphisms Lecture given by MD at the 1st Vienna Central European Seminar (Vienna, Austria, 26-28 Nov. 2004) (Preprint hep-th/0411224)
50. d and the equivalence of quantum field theories Nucl. Phys. B 581 559 (Preprint hep-th/0003018)
51. Wess J 2004 Deformed coordinate spaces: derivatives Lecture given at the Balkan Workshop BW2003 (Vrnjačka Banja, Serbia, Aug. 2003) (Preprint hep-th/0408080)
52. θ Nucl. Phys. B 717 387-403 (Preprint hep-th/0409012)
53. Chaichian M, Kulish P, Nishijima K and Tureanu A 2004 On a Lorentz-invariant interpretation of noncommutative space-time and its implications on noncommutative QFT Phys. Lett. B 604 98 (Preprint hep-th/0408069)
54. Matlock P 2005 Non-commutative geometry and twisted conformal symmetry Preprint hep-th/0504084
55. Calmet X 2005 Space-time symmetries of noncommutative spaces Phys. Rev. D 71 085012 (Preprint hep-th/0411147)