Initial time singularities in nonequilibrium evolution of condensâtes and their resolution in the linearized approximation

Physical Review D

Volumn 63, Issue 4, 2001, Pages

  Baacke, J ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BIOLISTIC TRANSFORMATION; CALCULATION; DYNAMICS; EVOLUTION; LINEAR SYSTEM; MATHEMATICAL ANALYSIS; MEASUREMENT; PHYSICS; QUANTUM MECHANICS; THEORY;

EID: 0035081841     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.63.045023     Document Type: Article

References (69)

1. For recent reviews on the QCD phase transitions and aspects of relativistic heavy ion collisions see, for example, J. W. Harris and B. Muller, Annu. Rev. Nucl. Part. Sei. 46, 71 (1996);
2. B. Muller, in Particle Production in Highly Excited Matter, edited by H. H. Gutbrod and J. Rafelski (NATO Advanced Study Institute, Series B: Physics, Vol. 303) (Plenum, New York, 1993);
3. B. Muller, The Physics of the Quark Gluon Plasma, Lecture Notes in Physics Vol. 225 (Springer-Verlag, Berlin, Heidelberg, 1985);
4. K. Rajagopal, in Quark-Gluon Plasma 2, edited by R. C. Hwa (World Scientific, Singapore, 1995);
5. H. Meyer-Ortmanns, Rev. Mod. Phys. 68, 473 (1996).
6. E. C. G. Stueckelberg, Phys. Rev. 81, 130 (1951).
7. See also, N. N. Bogoliubov and D. V. Shirkov, Quantum Fields (Benjamin, New York, 1983).
8. F. Cooper, S. Habib, Y. Kluger, E. Mottola, J. P. Paz, and P. R. Anderson, Phys. Rev. D 50, 2848 (1994);
9. F. Cooper, Y. Kluger, E. Mottola, and J. P. Paz, ibid. 51, 2377 (1995);
10. Y. Kluger, F. Cooper, E. Mottola, and J. P. Paz, Nucl. Phys. A590, 581c (1995);
11. M. A. Lampen, J. F. Dawson, and F. Cooper, Phys. Rev. D 54, 2213 (1996);
12. F. Cooper, Y. Kluger, and E. Mottola, Phys. Rev. C 54, 3298 (1996).
13. D. Boyanovsky, H. J. de Vega, and R. Holman, Nonequilibriuni Dynamics of Phase Transitions: From the Early Universe to Cltiral Condensâtes, Second Paris Cosmology Colloquium: Proceedings, edited by H. J. de Vega and N. Sanchez (World Scientific, Singapore, 1995);
14. D. Boyanovsky, D. Cormier, H. J. de Vega, R. Holman, and S. P. Kumar, in Out of Equilibrium Fields in Inflationary Dynamics: Density Fluctuations, Proceedings of the Vlth Erice Chalonge School on Astrofundamental Physics, edited by N. Sanchez and A. Zichichi (Kluwer, Dordrecht, 1998);
15. D. Boyanovsky, H. J. de Vega, and R. Holman, in Erice Lectures on Inflationary Reheating, Proceedings of the 5th Erice Chalonge School on Astrofundamental Physics, edited by N. Sanchez and A. Zichichi (World Scientific, Singapore, 1997), and references therein.
16. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961).
17. F. Cooper and E. Mottola, Mod. Phys. Lett. A 2, 635 (1987); Phys. Rev. D 36,3114 (1987).
18. J. Baacke, K. Heitmann, and C. Patzold, Phys. Rev. D 56, 6556 (1997).
19. S. A. Ramsey, B. L. Hu, and A. M. Stylianopoulos, Phys. Rev. D 57, 6003 (1998);
20. S. A. Ramsey and B. L. Hu, ibid. 56, 678 (1997).
21. A. A. Anselm and M. G. Ryskin, Phys. Lett. B 266, 482 (1991);
22. J.-P. Blaizot and A. Krzywicki, Phys. Rev. D 46, 246 (1992);
23. J. D. Bjorken, Int. J. Mod. Phys. A 7, 4189 (1992); Acta Phys. Pol. B 23, 561 (1992);
24. G. Amelino-Camelia, J. D. Bjorken, and S. E. Larsson, Phys. Rev. D 56, 6942 (1997);
25. J. D. Bjorken, Acta Phys. Pol. B 28, 2773 (1997);
26. A. Anselm, Phys. Lett. B 217, 169 (1989);
27. K. Rajagopal and F. Wilczek, Nucl. Phys. B399, 395 (1993); B404, 577 (1993);
28. S. Gavin, A. Gocksch, and R. D. Pisarski, Phys. Rev. Lett. 72, 2143 (1994);
29. S. Gavin and B. Muller, Phys. Lett." B 329, 486 (1994);
30. Z. Huang and X.-N. Wang, Phys. Rev. D 49, 4335 (1994);
31. Z. Huang, M. Suzuki, and X-N. Wang, ibid. 50, 2277 (1994);
32. Z. Huang and M. Suzuki, ibid. 53, 891 (1996);
33. M. Asakawa, Z. Huang, and X. N. Wang, Phys. Rev. Lett. 74, 3126 (1995);
34. D. Boyanovsky, H. J. de Vega, and R. Holman, Phys. Rev. D 51, 734 (1995);
35. F. Cooper, Y. Kluger, E. Mottola, and J. P. Paz, ibid. 51, 2377 (1995);
36. Y. Kluger, F. Cooper, E. Mottola, J. P. Paz, and A. Kovner, Nucl. Phys. A590, 581 (1995);
37. J. Randrup, ibid. A616, 531 (1997); Phys. Rev. Lett. 77, 1226 (1996);
38. H. Minakata and B. Muller, Phys. Lett. B 377, 135 (1996);
39. M. Asakawa, H. Minakata, and B. Muller, Phys. Rev. D 58, 094011 (1998);
40. D. Boyanovsky, H. J. de Vega, R. Holman, and S. Prem Kumar, ibid. 56, 3929 (1997); 56, 5233 (1997).
41. D. Boyanovsky, H. J. de Vega, and R. Holman, Phys. Rev. D 51, 734 (1995);
42. D. Boyanovsky, D.-S. Lee, and A. Singh, ibid. 48, 800 (1993);
43. D. Boyanovsky, H. J. de Vega, R. Holman, S. Prem Kumar, and R. D. Pisarski, ibid. 57, 3653 (1998).
44. Y. Tsue, D. Vautherin, and T. Matsui, Prog. Theor. Phys. 102, 343 (1999);
45. D. Vautherin and T. Matsui, Phys. Lett. B 437, 137 (1998).
46. D. Boyanovsky, F. Cooper, H. J. de Vega, and P. Sodano, Phys. Rev. D 58, 025007 (1998).
47. F. Cooper, S. Habib, Y. Kluger, and E. Mottola, Phys. Rev. D 55, 6471 (1997);
48. Y. Kluger, J. M. Eisenberg, B. Svetitsky, F. Cooper, and E. Mottola, ibid. 45, 4659 (1992); Phys. Rev. Lett. 67, 2427 (1991).
49. J. Baacke, K. Heitmann, and C. Paetzold, Phys. Rev. D 55, 7815 (1997).
50. G. Aarts and J. Smit, hep-ph/9902231 ; Nucl. Phys. B555, 355 (1999); hep-ph/9809340; Phys. Rev. D 61, 025002 (2000).
51. D. Boyanovsky, M. D'Attanasio, H. J. de Vega, and R. Holman, Phys. Rev. D 54, 1748 (1996).
52. D. Boyanovsky, M. D'Attanasio, H. J. de Vega, R. Holman, and D.-S. Lee, Phys. Rev. D 52, 6805 (1995); New Aspects of Reheating, String Gravity and Physics at the Planck Energy Scale: Proceedings of the NATO AS I at Erice, Italy, edited by N. Sanchez and A. Zichichi (Kluwer, Dordrecht, 1996), p. 451.
53. J. Baackc, K. Heitmann, and C. Pätzold, Phys. Rev. D 57, 6398 (1998); 57, 6406 (1998).
54. J. Baacke, K. Heitmann, and C. Pätzold, Phys. Rev. D 58, 125013 (1998).
55. K. Symanzik, Nucl. Phys. B190, 1 (1981).
56. V. P. Maslov and O. Yu. Shvedov, Theor. Math. Phys. 114, 184 (1998).
57. J. Schwinger, J. Math. Phys. 2, 407 (1961);
58. K. T. Mahanthappa, Phys. Rev. 126, 329 (1962);
59. P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 41, 12 (1963);
60. A. Niemi and G. Semenoff, Ann. Phys. (N.Y.) 152, 105 (1984);
61. N. P. Landsmann and C. G. van Weert, Phys. Rep. 145, 141 (1987);
62. E. Calzetta and B. L. Hu, Phys. Rev. D 35, 495 (1987); 37, 2838 (1990);
63. J. P. Paz, ibid. 41, 1054 (1990); 42, 529 (1990).
64. L. V. Keldysh, Zh. Eksp. Teor. Fiz. 20, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)];
65. K. Chou, Z. Su, B. Hao, and L. Yu, Phys. Rep. 118, l (1985).
66. D. Boyanovsky, H. J. de Vega, R. Holman, and M. Simionato, Phys. Rev. D 60, 065003 (1999).
67. S.-Y. Wang, D. Boyanovsky, H. J. de Vega, D.-S. Lee, and Y. J. Ng, Phys. Rev. D 61, 065007 (2000);
68. D. Boyanovsky, H. J. de Vega, D.-S. Lee, Y. J. Ng, and S.-Y. Wang, ibid. 59, 105001 (1999).
69. The extra factor s is introduced so as to make Gfs a function of 2 J .