Schwinger-Dyson approach to nonequilibrium classical field theory

Physical Review D

Volumn 64, Issue 12, 2001, Pages

  Blagoev, Krastan B ^a   Cooper, Fred ^b   Dawson, John F ^c   Mihaila, Bogdan ^d  

^a BOSTON COLLEGE   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c University of New Hampshire   (United States)

^d ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CORRELATION FUNCTION; DENSITY; MATHEMATICAL ANALYSIS; MOLECULAR EVOLUTION; OSCILLATION; QUANTUM THEORY; SIMULATION;

EID: 0035893854     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.64.125003     Document Type: Article

References (66)

1. A.K. Kerman and S.E. Koonin, Ann. Phys. (N.Y.) 100, 332 (1976);
2. R. Jackiw and A.K. Kerman, Phys. Lett. 71A, 158 (1979);
3. A.H. Guth and S.-Y. Pi, Phys. Rev. D 32, 1899 (1985);
4. F. Cooper, S.-Y. Pi, and P. Stancioff, Phys. Rev. D ibid. 34, 3831 (1986);
5. S.-Y. Pi and M. Samiullah, Phys. Rev. D ibid. 36, 3128 (1987).
6. D. Boyanovsky and HJ. de Vega, Phys. Rev. D 47, 2343 (1993);
7. D. Boyanovsky, H.J. de Vega, R. Holman, D.-S. Lee, and A. Singh, Phys. Rev. D ibid. 51, 4419 (1995);
8. D. Boyanovsky, H.J. de Vega, R. Holman, and J. Salgado, Phys. Rev. D ibid. 54, 7570 (1996);
9. D. Boyanovsky, D. Cormier, H.J. de Vega, R. Holman, A. Singh, and M. Srednicki, Phys. Rev. D ibid. 56, 1939 (1997);
10. D. Boyanovsky, M. D'Attanasio, H.J. de Vega, R. Holman, and D.S. Lee, Phys. Rev. D ibid. 52, 6805 (1995);
11. D. Vautherin and T. Matsui, Phys. Rev. D ibid. 55, 4492 (1997);
12. D. Boyanovsky, H.J. de Vega, R. Holman, and J. Salgado, Phys. Rev. D ibid. 57, 7388 (1998).
13. F. Cooper and E. Mottola, Phys. Rev. D 36, 3114 (1987);
14. F. Cooper, Y. Kluger, E. Mottola, and J.P. Paz, Phys. Rev. D ibid. 51, 2377 (1995);
15. Y. Kluger, F. Cooper, E. Mottola, J.P. Paz, and A. Kovner, Nucl. Phys. A590, 581c (1995);
16. M.A. Lampert, J.F. Dawson and F. Cooper, Phys. Rev. D 54, 2213 (1996);
17. F. Cooper, Y. Kluger, and E. Mottola, Phys. Rev. C 54, 3298 (1996).
18. A. Chodos, F. Cooper, W-j. Mao, H. Minakata, and A. Singh, Phys. Rev. D 61, 045011 (2000);
19. A. Chodos, F. Cooper, W-j. Mao, H. Minakata, and A. Singh, Phys. Rev. D 63, 096010 (2001).
20. C. Wetterich, Phys. Rev. Lett. 78, 3598 (1997);
21. L. Bettencourt and C. Wetterich, Phys. Lett. B 430, 140 (1998); hep-ph/9805360;
22. G.F. Bonini and C. Wetterich, Phys. Rev. D 60, 105026 (1999).
23. G. Aarts, G.F. Bonini, and C. Wetterich, Phys. Rev. D 63, 025012 (2001).
24. F. Cooper, S. Habib, Y. Kluger, E. Mottola, J. Paz, and P. Anderson, Phys. Rev. D 50, 2848 (1994);
25. F. Cooper, J.F. Dawson, S. Habib, Y. Kluger, D. Meredith, and H. Shepard, Physica D 83, 74 (1995).
26. B. Mihaila, T. Athan, F. Cooper, J.F. Dawson, and S. Habib, Phys. Rev. D 62, 125015 (2000).
27. J.M. Luttinger and J.C. Ward, Phys. Rev. 118, 1417 (1960);
28. G. Baym, Phys. Rev. ibid. 127, 1391 (1962);
29. B. Vanderheyden and G. Baym, in Progress in Nonequilibrium Green's functions, edited by M. Bonitz (World Scientific, Singapore, in press), hep-ph/0002291.
30. M.M. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D 10, 2428 (1974).
31. C. De Dominicis, J. Math. Phys. 3, 983 (1962);
32. C. De Dominicis and P.C. Martin, J. Math. Phys. ibid. 5, 14 (1964);
33. C. De Dominicis and P.C. Martin, J. Math. Phys. 5, 31 (1964).
34. H.D. Dahmen and G. Jona-Lasinio, Nuovo Cimento A 52, 807 (1967);
35. H.D. Dahmen and G. Jona-Lasinio, Nuovo Cimento A 62, 889 (1969).
36. A.N. Vasil'ev and A.K. Kazanskii, Teor. Mat. Fiz. 12, 352 (1972);
37. A.N. Vasil'ev and A.K. Kazanskii, Teor. Mat. Fiz. 14, 289 (1973).
38. J. Berges and J. Cox, "Thermalization of Quantum Fields from Time-Reversal Invariant Evolution Equations," hep-ph/0006160.
39. C.M. Bender, F. Cooper, and G.S. Guralnik, Ann. Phys. (N.Y.) 109, 165 (1977).
40. B. Mihaila, F. Cooper, and J.F. Dawson, Phys. Rev. D 63, 096003 (2001).
41. R.H. Kraichnan, J. Fluid Mech. 5, 497 (1959);
42. J. Math. Phys. 2, 124 (1961);
43. J. Math. Phys. 3, 205 (1962).
44. P.C. Martin, E.D. Siggia, and H.A. Rose, Phys. Rev. A 8, 423 (1973);
45. H.A. Rose, Harvard thesis, 1974.
46. J. Schwinger, J. Math. Phys. 2, 407 (1961);
47. P.M. Bakshi and K.T. Mahanlhappa, J. Math. Phys. ibid. 4, 1 (1963);
48. P.M. Bakshi and K.T. Mahanlhappa, J. Math. Phys. 4, 12 (1963);
49. L.V. Keldysh, Zh. Éksp. Teor. Fiz. 47, 1515 (1964)
50. [Sov. Phys. JETP 20, 1018 (1965)];
51. G. Zhou, Z. Su, B. Hao, and L. Yu, Phys. Rep. 118, 1 (1985).
52. F. Cooper, A. Khare, and H. Rose, Phys. Lett. B 515, 463 (2001).
53. G. Parisi, Statistical Field Theory (Addison-Wesley, New York, 1988).
54. G. Aarts and J. Smit, Phys. Lett. B 393, 395 (1997).
55. W. Buchmüller and A. Jakovác, Phys. Lett. B 407, 39 (1997).
56. W. Buchmüller and A. Jakovác, Nucl. Phys. B521, 219 (1998).
57. A.B. Migdal, Sov. Phys. JETP 7, 996 (1958).
58. J.R. Schrieffer, Theory of Superconductivity (Benjamin, New York, 1964).
59. E.A. Calzetta and B.L. Hu, Phys. Rev. D 37, 2878 (1988);
60. E.A. Calzetta, B.L. Hu, and S.A. Ramsey, Phys. Rev. D ibid. 61, 125013 (2000).
61. B. Mihaila, J.F. Dawson, and F. Cooper, Phys. Rev. D 56, 5400 (1997).
62. B. Mihaila and I. Mihaila, physics/9901005.
63. J. Berges, "Controlled nonperturative dynamics of quantum fields out of equilibrium," hep-ph/0105311.
64. F. Cooper, G. Guralnik, R.W. Haymaker, and K. Tamvakis, Phys. Rev. D 20, 3336 (1979).
65. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge University Press, Cambridge, England, 1992), p. 833.
66. 2 in our initial density matrix is allowable. However, if we were to study the quantum version of this problem, we would have to use the renormalized mass and not the bare mass in the initial density matrix.