Reformulation of QCD in the language of general relativity

Journal of Mathematical Physics

Volumn 37, Issue 11, 1996, Pages 5351-5367

  Lunev, F A ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030487339     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531729     Document Type: Article

References (45)

1. C. J. Isham, A. Salam, and J. Strathdee, Phys. Rev. D 3, 867 (1971).
2. E. W. Mielke, Geometrodynamics of Gauge Fields (Academie, Berlin, 1987).
3. F. W. Hehl, J. Nitch, and P. von der Heyde, in General Relativity and Gravitation - One Hundred Years After the Birth of Albert Einstein, (Plenum, New York, 1980), p. 329.
4. A. Salam, ICTP preprint IC/71/3 (unpublished); C. J. Isham, A. Salam, and J. Strathdee, Phys. Rev. D 8, 2600 (1973); C. Sivaram and K. P. Singha, Phys. Rep. 51, 111 (1979); A. Salam and C. Sivaram, Mod. Phys. Lett. A 8, 321 (1993).
5. A. Salam, ICTP preprint IC/71/3 (unpublished); C. J. Isham, A. Salam, and J. Strathdee, Phys. Rev. D 8, 2600 (1973); C. Sivaram and K. P. Singha, Phys. Rep. 51, 111 (1979); A. Salam and C. Sivaram, Mod. Phys. Lett. A 8, 321 (1993).
6. A. Salam, ICTP preprint IC/71/3 (unpublished); C. J. Isham, A. Salam, and J. Strathdee, Phys. Rev. D 8, 2600 (1973); C. Sivaram and K. P. Singha, Phys. Rep. 51, 111 (1979); A. Salam and C. Sivaram, Mod. Phys. Lett. A 8, 321 (1993).
7. A. Salam, ICTP preprint IC/71/3 (unpublished); C. J. Isham, A. Salam, and J. Strathdee, Phys. Rev. D 8, 2600 (1973); C. Sivaram and K. P. Singha, Phys. Rep. 51, 111 (1979); A. Salam and C. Sivaram, Mod. Phys. Lett. A 8, 321 (1993).
8. E. W. Mielke, Int. J. Theor. Phys. 19, 189 (1980).
9. J. C. Huang and P. W. Dennis, Phys. Rev. D 21, 910 (1980); 23, 1723 (1981); 24, 35 (1981).
10. J. C. Huang and P. W. Dennis, Phys. Rev. D 21, 910 (1980); 23, 1723 (1981); 24, 35 (1981).
11. J. C. Huang and P. W. Dennis, Phys. Rev. D 21, 910 (1980); 23, 1723 (1981); 24, 35 (1981).
12. Y. Ne'eman and Dj. Sijacki, Phys. Lett. B 247, 571 (1990); 276, 173 (1992); preprint CERN-TH. 7461/94 (unpublished); preprint TAUP N232-94 (unpublished).
13. Y. Ne'eman and Dj. Sijacki, Phys. Lett. B 247, 571 (1990); 276, 173 (1992); preprint CERN-TH. 7461/94 (unpublished); preprint TAUP N232-94 (unpublished).
14. M. Yu. Kuchiev, Europhys. Lett. 28, 539 (1994).
15. F. A. Lunev, Phys. Lett. B. 295, 99 (1992); Theor. Math. Phys. 94, 66 (1993).
16. F. A. Lunev, Phys. Lett. B. 295, 99 (1992); Theor. Math. Phys. 94, 66 (1993).
17. Interesting approach to unification of YM theory and general relativity in three dimensions was proposed by Peldan. (See P. Peldan, Nucl. Phys. B 395, 239 (1993)). However, it is not clear, how to generalize this approach on 4D case.
18. K. Johnson, in QCD - 20 Years Later (World Scientific, Singapore, 1993), p. 795.
19. F. A. Lunev, Phys. Lett. B 311, 273 (1993).
20. F. A. Lunev, Phys. At. Nucl. 56, 1591 (1993) [Yad. Fiz. 56, 238 (1993)].
21. F. A. Lunev, Phys. At. Nucl. 56, 1591 (1993) [Yad. Fiz. 56, 238 (1993)].
22. E. W. Mielke, Yu. Obukhov, and F. W. Hehl, Phys. Lett. A 192, 153 (1994).
23. M. Bauer, D. Z. Freedman, and P. E. Haagensen, Nucl. Phys. B 428, 147 (1994).
24. P. E. Haagensen and K. Johnson, Nucl. Phys. B (to be published), hep-th/9408164.
25. V. Radovanovic and D. Sijacki (unpublished), hep-th/9411002.
26. D. Z. Freedman, P. E. Haagensen, K. Johnson, and J.-I. Lattore, preprint CERN-TH 7010/93 (unpublished).
27. D. Singleton (unpublished), hep-th/9501052,950197,9502116.
28. A. Salam and J. Strathdee, Phys. Rev. D 16, 2668 (1977).
29. It is necessary to note that effective "metric" constructed from YM fields was introduced, first, by Halpern in his investigations of self-dual sector of 4D YM theory. (See M. B. Halpern, Phys. Rev. D 16, 3515 (1977)). Halpern "metric" is biliniar form of self-dual field strengths that is very similar to Eq. (8). So Halpern's results can be considered as prototype of ones obtained in Refs. 9 and 11. But, in contrast to metric (8), Halpem "metric" is not second rank space-time tensor and so it is not an analog of metric in general relativity.
30. J. F. Plebanski, J. Math. Phys. 18, 2511 (1977).
31. After the completion of this paper author learned about recent works by Robinson (D. C. Robinson, Class. Quant. Grav. 11, L157 (1994); King's College preprint (1995)) in which the analogy between general relativity and YM theory in Plebanski approach is considerably clarified. The relations between these results and ones obtained in the present paper need further investigations.
32. T. Jacobson and L. Smolin, Class. Quant. Grav. 5, 583 (1988).
33. J. Samuel, Pranama 28, L429 (1987).
34. H. Urbantke, J. Math. Phys. 25, 2321 (1984).
35. G. Harnett, J. Math. Phys. 32, 84 (1991); J. Phys. A 25, 5649 (1992).
36. G. Harnett, J. Math. Phys. 32, 84 (1991); J. Phys. A 25, 5649 (1992).
37. G. 't Hooft, Nucl. Phys. B 357, 211 (1991).
38. I. Bengtsson, preprint USITP 95-2 (unpublished), gr-qc/9502010.
39. A. Ashtekar, Phys. Rev. Lett. 57, 2244 (1986); Phys. Rev. D 36, 1587 (1987).
40. A. Ashtekar, Phys. Rev. Lett. 57, 2244 (1986); Phys. Rev. D 36, 1587 (1987).
41. An attempt to develop the formalism for unified description of YM and gravity fields in the spirit of Ashtekar phase space approach was done in works S. Chakraborty and P. Peldan, Phys. Rev. Lett. 73, 1195 (1994); Int. J. Mod. Phys. D 3, 695 (1195). However, this theory gives the conventional YM theory only in the lowest order in the fields and so it is hard to make consistent its predictions with ones of the Standard Model.
42. An attempt to develop the formalism for unified description of YM and gravity fields in the spirit of Ashtekar phase space approach was done in works S. Chakraborty and P. Peldan, Phys. Rev. Lett. 73, 1195 (1994); Int. J. Mod. Phys. D 3, 695 (1195). However, this theory gives the conventional YM theory only in the lowest order in the fields and so it is hard to make consistent its predictions with ones of the Standard Model.
43. R. Capovilla, J. Dell, T. Jacobson, and L. Mason, Class. Quant. Grav. 8, 41 (1991).
44. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961).
45. F. A. Lunev, Mod. Phys. Lett. A 9, 2281 (1994).