Hamiltonian reduction of [Formula presented] Dirac-Yang-Mills mechanics

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 57, Issue 12, 1998, Pages 7488-7500

  Khvedelidze, A M ^b,d   Mladenov, D M ^b  

^a TBILISI STATE UNIVERSITY   (Georgia)

^b JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

^c UNIVERSITY OF ROSTOCK   (Germany)

^d A RAZMADZE MATHEMATICAL INSTITUTE   (Georgia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001330146     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.57.7488     Document Type: Article

References (49)

1. P. A. M. Dirac, Lectures on Quantum Mechanics, Belfer Graduate School of Science (Yeshiva University Press, New York, 1964).
2. N. P. Konopleva and V. N. Popov, Gauge Fields (Atomizdat, Moscow, 1972) (in Russian).
3. K. Sundermeyer, Constrained Dynamics, Lecture Notes in Physics Vol. 169 (Springer-Verlag, Berlin-Heidelberg-New York, 1982).
4. D. M. Gitman and I. V. Tyutin, Quantization of Fields With Constraints (Springer-Verlag, Bonn, 1990).
5. M. Henneaux, C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, NJ, 1992).
6. C. N. Yang and R. L. Mills, Phys. Rev. 96, 191 (1954).
7. V. N. Gribov, Nucl. Phys. B139, 1 (1978);
8. I. M. Singer, Commun. Math. Phys. 60, 7 (1978);
9. I. M. SingerPhys. Scr. 24, 817 (1981);
10. O. Babelon and C. M. Viallet, Commun. Math. Phys. 81, 515 (1981);
11. Commun. Math. Phys.M. S. Narasimhan and T. R. Ramadas, 67, 21 (1979);P. K. Mitter, in Recent Developments in Gauge Theories, edited by G. ’t Hooft (Plenum, New York, 1980);
12. M. F. Atyah, Geometry of Yang-Mills Fields (Scuola Normale Superiore, Pisa, 1979);V. Moncrief, in Differential Geometrical Methods in Mathematical Physics, edited by P. L. Garcia et al., Lecture Notes in Mathematics, Vol. 836 (Springer, Berlin, 1980), p. 276.
13. J. Goldstone and R. Jackiw, Phys. Lett. 74B, 81 (1978).
14. V. Baluni and B. Grossman, Phys. Lett. 78B, 226 (1978).
15. A. G. Izergin, V. F. Korepin, M. E. Semenov-Tyan-Shanskii, and L. D. Faddeev, Teor. Mat. Fiz. 38, 3 (1979).
16. A. Das, M. Kaku, and P. K. Townsend, Nucl. Phys. B149, 109 (1979).
17. N. H. Christ and T. D. Lee, Phys. Rev. 22, 939 (1980).
18. V. N. Pervushin, Teor. Mat. Fiz. 45, 327 (1980).
19. Yu. Simonov, Sov. J. Nucl. Phys. 41, 835 (1985).
20. V. V. Vlasov, V. A. Matveev, A. N. Tavkhelidze, S. Yu. Khlebnikov, and M. E. Shaposhnikov, Phys. Elem. Part. Nucl. 18, 5 (1987).
21. E. T. Newman and C. Rovelli, Phys. Rev. Lett. 69, 1300 (1992).
22. D. Freedmann, P. Haagensen, K. Johnson, and J. Latorre, MIT Report No. CTP 2238 (1993).
23. M. Lavelle and D. McMullan, Phys. Rep. 279, 1 (1997).
24. A. M. Khvedelidze and V. N. Pervushin, Helv. Phys. Acta 67, 637 (1994).
25. S. G. Matinyan, G. K. Savvidy, and N. G. Ter-Arutyunyan-Savvidy, Sov. Phys. JETP 53, 421 (1981).
26. H. M. Asatryan and G. K. Savvidy, Phys. Lett. 99A, 290 (1983).
27. M. A. Soloviev, Teor. Mat. Fiz. 73, 3 (1987).
28. M. J. Gotay, J. Geom. Phys. 6, 349 (1989).
29. B. Dahmen and B. Raabe, Nucl. Phys. B384, 352 (1992).
30. S. Shanmugadhasan, J. Math. Phys. 14, 677 (1973).
31. E. Cartan, Lecons sur les invariant integraux (Hermann, Paris, 1922).
32. J. Marsden and A. Weinstein, Rep. Math. Phys. 5, 121 (1974).
33. P. Olver, Applications of Lie Groups to Differential Equations, Graduate Text in Mathematics (Springer-Verlag, New York-Berlin-Heidelberg-Tokyo, 1986).
34. V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Encyclopaedia of Mathematical Science, Vol. III, Dynamical Systems (Springer-Verlag, New York-Berlin, 1988).
35. A. M. Perelomov, Integrable Systems in Classical Mechanics and Lie’s Algebra (Nauka, Moscow, 1990) (in Russian).
36. P. A. M. Dirac, Rev. Mod. Phys. 21, 392 (1949).
37. L. D. Faddeev, Theor. Math. Phys. 1, 1 (1969).
38. P. A. M. Dirac, Phys. Rev. 114, 924 (1959).
39. E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, England, 1937).
40. I. A. Batalin and G. A. Vilkovisky, Nucl. Phys. B234, 106 (1984).
41. S. A. Gogilidze, A. M. Khvedelidze, and V. N. Pervushin, Phys. Rev. D 53, 2160 (1996).
42. S. A. Gogilidze, A. M. Khvedelidze, and V. N. Pervushin, J. Math. Phys. 37, 1760 (1996).
43. P. G. Bergman and I. Goldberg, Phys. Rev. 98, 531 (1955).
44. L. V. Prokhorov and S. V. Shabanov, Usp. Fiz. Nauk 161, 13 (1991).
45. G. K. Savvidy, Phys. Lett. 71B, 133 (1977).
46. Y. A. Arkhangelskii, Analitical Dynamics of Rigid Body (Nauka, Moscow, 1977) (in Russian).
47. H. Andoyer, Cours de mècanique cèleste (Gauthier-Villars, Paris, 1923), Vol. 1.
48. D. Blaschke, H.-P. Pavel, V. N. Pervushin, G. Röpke, and M. K. Volkov, Phys. Lett. B 397, 129 (1997);
49. H.-P. Pavel, D. Blaschke, V. N. Pervushin, G. Röpke, and M. K. Volkov, “Squeezed gluon condensate and the mass of the (Formula presented)” hep-ph/9706528.