Magnetic backgrounds and noncommutative field theory

International Journal of Modern Physics A

Volumn 19, Issue 12, 2004, Pages 1837-1861

  Szabo, Richard J ^a  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

Noncommutative field theory; Quantum gravity; Quantum Hall systems; String theory

Indexed keywords

CALCULATION; GEOMETRY; GRAVITY; INFRARED RADIATION; MAGNETIC FIELD; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; QUANTUM CHEMISTRY; REVIEW; ULTRAVIOLET RADIATION;

EID: 9344265560     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X04018099     Document Type: Review

References (78)

1. R. Peierls, Z. Phys. 80, 763 (1933).
2. H. S. Snyder, Phys. Rev. 71, 38 (1947).
3. A. Connes, M. R. Douglas and A. Schwarz, J. High Energy Phys. 9802, 003 (1998).
4. M. R. Douglas and C. M. Hull, J. High Energy Phys. 9802, 008 (1998).
5. G. Landi, F. Lizzi and R. J. Szabo, Commun. Math. Phys. 206, 603 (1999).
6. V. Schomerus, J. High Energy Phys. 9906, 030 (1999).
7. N. Seiberg and E. Witten, J. High Energy Phys. 9909, 032 (1999).
8. L. D. Landau and L. M. Lifschitz, Quantum Mechanics: Nonrelativistic Theory (Pergamon Press, Oxford, 1977).
9. L. Susskind, arXiv:hep-th/0101029.
10. A. P. Polychronakos, J. High Energy Phys. 0104, 011 (2001).
11. S. Hellerman and M. Van Raamsdonk, J. High Energy Phys. 0110, 039 (2001).
12. A. Konechny and A. Schwarz, Phys. Rep. 360, 353 (2002); arXiv:hep-th/0107251.
13. M. R. Douglas and N. A. Nekrasov, Rev. Mod. Phys. 73, 977 (2001).
14. R. J. Szabo, Phys. Rep. 378, 207 (2003).
15. R. Jackiw, Nucl. Phys. Proc. Suppl. B108, 30 (2002).
16. P. A. M. Dirac, Lectures on Quantum Mechanics (Yeshiva University Press, New York, 1964).
17. D. B. Fairlie, P. Fletcher and C. K. Zachos, J. Math. Phys. 31, 1088 (1990).
18. E. Brown, Phys. Rev. 133, 1038 (1963).
19. J. Zak, Phys. Rev. 134, 1602, 1607 (1964).
20. H. J. Grönewold, Physica 12, 405 (1946).
21. J. E. Moyal, Proc. Cambridge Phil. Soc. 45, 99 (1949).
22. S.-J. Rey, in Gravity, Gauge Theories and Strings (Les Houches, 2001), p. 587.
23. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Ann. Phys. 111, 61 (1978).
24. E. Witten, Nucl. Phys. B268, 253 (1986).
25. F. Lizzi and R. J. Szabo, J. High Energy Phys. Conf. Proc. corfu98/073, arXiv:hep-th/9904064.
26. S. Doplicher, K. Fredenhagen and J. E. Roberts, Phys. Lett. B331, 39 (1994).
27. D. J. Gross and P. F. Mende, Nucl. Phys. B303, 407 (1988).
28. G. Veneziano, Europhys. Lett. 2, 199 (1986).
29. D. Amati, M. Ciafaloni and G. Veneziano, Phys. Lett. B216, 41 (1989).
30. T. Yoneya, Progr. Theor. Phys. 103, 1081 (2000).
31. P. Hořava, Phys. Lett. B231, 251 (1989).
32. J. Dai, R. G. Leigh and J. Polchinski, Mod. Phys. Lett. A4, 2073 (1989).
33. J. Polchinski, Phys. Rev. Lett. 75, 4724 (1995).
34. M. R. Douglas, D. Kabat, P. Pouliot and S. H. Shenker, Nucl. Phys. B485, 85 (1997).
35. N. E. Mavromatos and R. J. Szabo, Phys. Rev. D59, 104018 (1999).
36. E. Witten, Nucl. Phys. B460, 33 (1996).
37. H. Aoki, N. Ishibashi, S. Iso, H. Kawai, Y. Kitazawa and T. Tada, Nucl. Phys. B565, 176 (2000).
38. S.-J. Rey and R. von Unge, Phys. Lett. B499, 215 (2001).
39. A. Abouelsaood, C. G. Callan, C. R. Nappi and S. A. Yost, Nucl. Phys. B280, 599 (1987).
40. J. Ambjørn, Y. M. Makeenko, G. W. Semenoff and R. J. Szabo, J. High Energy Phys. 0302, 026 (2003).
41. I. Chepelev and R. Roiban, J. High Energy Phys. 0005, 037 (2000).
42. I. Chepelev and R. Roiban, J. High Energy Phys. 0103, 001 (2001).
43. E. Langmann, R. J. Szabo and K. Zarembo, J. High Energy Phys. 0401, 017 (2004).
44. H. Grosse and R. Wulkenhaar, arXiv:hep-th/0401128.
45. D. Bahns, S. Doplicher, K. Fredenhagen and G. Piacitelli, Phys. Lett. B533, 178 (2002).
46. G. 't Hooft, Nucl. Phys. B72, 461 (1974).
47. D. Bessis, C. Itzykson and J.-B. Zuber, Adv. Appl. Math. 1, 109 (1980).
48. T. Filk, Phys. Lett. B376, 53 (1996).
49. N. Ishibashi, S. Iso, H. Kawai and Y. Kitazawa, Nucl. Phys. B573, 573 (2000).
50. S. Minwalla, M. Van Raamsdonk and N. Seiberg, J. High Energy Phys. 0002, 020 (2000).
51. M. M. Sheikh-Jabbari, Phys. Lett. B455, 129 (1999).
52. D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000).
53. F. Lizzi, R. J. Szabo and A. Zampini, J. High Energy Phys. 0108, 032 (2001).
54. D. J. Gross, A. Hashimoto and N. Itzhaki, Adv. Theor. Math. Phys. 4, 893 (2000).
55. E. Langmann and R. J. Szabo, Phys. Rev. D64, 104019 (2001).
56. F. Lizzi and R. J. Szabo, Chaos Solitons Fractals 10, 445 (1999).
57. N. Ishibashi, S. Iso, H. Kawai and Y. Kitazawa, Nucl. Phys. B583, 159 (2000).
58. Y. Okawa and H. Ooguri, Nucl. Phys. B599, 55 (2001).
59. A. Dhar and Y. Kitazawa, J. High Energy Phys. 0108, 044 (2001).
60. S. R. Das and S.-J. Rey, Nucl. Phys. B590, 453 (2000).
61. Y. Kiem, S.-J. Rey, H. Sato and J.-T. Yee, Eur. Phys. J. C22, 757 (2002).
62. Y. Kiem, S. Lee, S.-J. Rey and H.-T. Sato, Phys. Rev. D65, 046003 (2002).
63. M. M. Sheikh-Jabbari, Phys. Rev. Lett. 84, 5265 (2000).
64. S. M. Carroll, J. A. Harvey, V. A. Kostelecký, C. D. Lane and T. Okamato, Phys. Rev. Lett. 87, 141601 (2001).
65. I. Hinchliffe, H. Kersting and Y. L. Ma, arXiv:hep-ph/0205040.
66. M. Chaichian, M. M. Sheikh-Jabbari and A. Tureanu, Phys. Rev. Lett. 86, 2716 (2001).
67. X. Calmet, arXiv:hep-ph/0401097.
68. Z. Guralnik, R. Jackiw, S.-Y. Pi and A. P. Polychronakos, Phys. Lett. B517, 450 (2001).
69. G. Amelino-Camelia, L. Doplicher, S. Nam and Y. S. Reo, Phys. Rev. D67, 085008 (2003).
70. S. M. Girvin and R. S. Prange (eds.), The Quantum Hall Effect (Springer-Verlag, Berlin, 1987).
71. R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).
72. E. Fradkin, Field Theories of Condensed Matter Systems (Addison-Wesley, 1991).
73. S. Bahcall and L. Susskind, Int. J. Mod. Phys. B5, 2735 (1991).
74. E. Fradkin, V. Jejjala and R. G. Leigh, Nucl. Phys. B642, 483 (2002).
75. V. P. Nair and A. P. Polychronakos, Phys. Rev. Lett. 87, 030403 (2001).
76. M. Olshanetsky and A. M. Perelomov, Invent. Math. 31, 93 (1976).
77. A. P. Polychronakos, Phys. Lett. B266, 29 (1991).
78. O. Bergman, Y. Okawa and J. H. Brodie, J. High Energy Phys. 0111, 019 (2001).