Heat kernel of nonminimal gauge field kinetic operators on Moyal plane

International Journal of Modern Physics A

Volumn 22, Issue 1, 2007, Pages 181-202

  Strelchenko, Alexei ^a  

^a OLES HONCHAR DNIPRO NATIONAL UNIVERSITY   (Ukraine)

Author keywords

Classical and semiclassical techniques in gauge field theories; Heat kernel; Noncommutative field theory

Indexed keywords

EID: 33846634265     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X07034921     Document Type: Review

References (57)

1. R. Endo, Prog. Theor. Phys. 71, 1366 (1984).
2. V. Gayral, J. M. Gracia-Bondia and F. R. Ruiz, Phys. Lett. B 610, 141 (2005).
3. P. B. Gilkey, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem (CRC Press, Boca Raton, Florida, 1994).
4. N. Berline, E. Getzler and M. Vergne, Heat Kernels and Dirac Operators (Springer-Verlag, Berlin, 1992).
5. K. Kirsten, Spectral Functions in Mathematics and Physics (Chapman & Hall/CRC, Boca Raton, Florida, 2001).
6. D. V. Vassilevich, Phys. Rep. 388, 279 (2003).
7. D. V. Vassilevich, Lett. Math. Phys. 67, 185 (2004).
8. V. Gayral and B. Iochum, J. Math. Phys. 46, 043503 (2005).
9. V. Gayral, Ann. Henri Poincaré 6, 991 (2005).
10. D. V. Vassilevich, Nucl. Phys. B 715, 695 (2005).
11. D. V. Vassilevich, J. High Energy Phys. 0508, 085 (2005).
12. V. Gayral, B. Iochum and D. V. Vassilevich, Heat kernel and number theory on NC-torus, hep-th/0607078.
13. I. Chepelev and R. Roiban, J. High Energy Phys. 0005, 037 (2000).
14. S. Minwalla, M. Van Raamsdonk and N. Seiberg, J. High Energy Phys. 0002, 020 (2000).
15. I. Y. Aref'eva, D. M. Belov and A. S. Koshelev, Phys. Lett. B 476, 431 (2000).
16. A. O. Barvinsky and G. A. Vilkovisky, Phys. Rep. 119, 1 (1985).
17. V. P. Gusynin, E. V. Gorbar and V. V. Romankov, Nucl. Phys. B 362, 449 (1991).
18. V. P. Gusynin and E. V. Gorbar, Phys. Lett. B 270, 29 (1991).
19. E. I. Guendelman, A. Leonidov, V. Nechitailo and D. A. Owen, Phys. Lett. B 324, 160 (1994).
20. R. Endo, Class. Quantum Grav. 12, 1157 (1995).
21. S. Alexandrov and D. V. Vassilevich, J. Math. Phys. 37, 5715 (1996).
22. I. G. Avramidi and T. Branson, Rev. Math. Phys. 13, 847 (2001).
23. I. G. Avramidi, Non-Laplace type operators on manifolds with boundary, math-ph/0509023.
24. L. Alvarez-Gaume and J. L. F. Barbon, Int. J. Mod. Phys. A 16, 1123 (2001).
25. A. Das, J. Frenkel, S. H. Pereira and J. C. Taylor, Phys. Lett. B 577, 76 (2003).
26. B. S. DeWitt, The Dynamical Theory of Groups and Fields (Gordon and Breach, New York, 1965).
27. J. Schwinger, Phys. Rev. 82, 664 (1951).
28. R. T. Seeley, Proc. Symp. Pure Math. 10, 288 (1967).
29. P. B. Gilkey, J. Diff. Geom. 10, 601 (1975).
30. E. Megias, E. Ruiz Arriola and L. L. Salcedo, Phys. Rev. D 69, 116003 (2004).
31. N. K. Nielsen and P. van Nieuwenhuizen, Phys. Rev. D 39, 3183 (1988).
32. T. P. Branson, P. B. Gilkey and D. V. Vassilevich, J. Math. Phys. 39, 1040 (1998)
33. [Erratum: ibid. 41, 3301 (2000)).
34. R. I. Nepomechie, Phys. Rev. D 31, 3291 (1985).
35. A. Armoni, Nucl. Phys. B 593, 229 (2001).
36. M. Chaichian, P. P. Kulish, K. Nishijima and A. Tureanu, Phys. Lett. B 604, 98 (2004).
37. M. Chaichian, P. Presnajder and A. Tureanu, Phys. Rev. Lett. 94, 151602 (2005).
38. J. Wess, Deformed coordinate spaces: Derivatives, hep-th/0408080.
39. R. Oeckl, Nucl. Phys. B 581, 559 (2000).
40. F. Koch and E. Tsouchnika, Nucl. Phys. B 717, 387 (2005).
41. P. Matlock, Phys. Rev. D 71, 126007 (2005).
42. P. Aschieri, C. Blohmann, M. Dimitrijevic, F. Meyer, P. Schupp and J. Wess, Class. Quantum Grav. 22, 3511 (2005).
43. B. M. Zupnik, Phys. Lett. B 627, 208 (2005).
44. B. M. Zupnik, Reality in noncommutative gravity, hep-th/0512231.
45. F. Lizzi, S. Vaidya and P. Vitale, Phys. Rev. D 73, 125020 (2006).
46. A. Kobakhidze, Theta-twisted gravity, hep-th/0603132.
47. A. Tureanu, Phys. Lett. B 638, 296 (2006).
48. J. Zahn, Phys. Rev. D 73, 105005 (2006).
49. D. V. Vassilevich, Mod. Phys. Lett. A 21, 1279 (2006).
50. P. Aschieri, M. Dimitrijevic, F. Meyer, S. Schraml and J. Wess, Twisted gauge theories, hep-th/0603024.
51. M. Chaichian and A. Tureanu, Phys. Lett. B 637, 199 (2006).
52. M. Chaichian, A. Tureanu and G. Zet, Twist as a symmetry principle and the non-commutative gauge theory formulation, hep-th/0607179.
53. L. Alvarez-Gaume, F. Meyer and M. A. Vazquez-Mozo, Comments on noncommutative gravity, hep-th/0605113.
54. N. Seiberg and E. Witten, J. High Energy Phys. 9909, 032 (1999).
55. J. Gomis and T. Mehen, Nucl. Phys. B 591, 265 (2000).
56. N. Seiberg, L. Susskind and N. Toumbas, J. High Energy Phys. 0006, 044 (2000).
57. M. Chaichian, K. Nishijima and A. Tureanu, Phys. Lett. B 568, 146 (2003).