- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Effective Lagrangian and the back-reaction problem in a self-interacting O(N) scalar theory in curved spacetime

E. Elizalde

K. Kirsten and S. D. Odintsov

  • Departament d’Estructura i Constituents de la Matèria i Institut de Física d’Altes Energies, Faculty of Physics, University of Barcelona, Diagonal 647, 08028 Barcelona, Catalonia, Spain
  • Center for Advanced Studies, Consejo Superior de Investigaciones Científicás, Camí de Santa Bàrbara, 17300 Blanes, Catalonia, Spain

  • Departament d’Estructura i Constituents de la Matèria, Faculty of Physics, University of Barcelona, Diagonal 647, 08028 Barcelona, Catalonia, Spain

PDF

Phys. Rev. D 50, 5137 – Published 15 October, 1994

DOI: https://doi.org/10.1103/PhysRevD.50.5137

Abstract

A derivation of the one-loop effective Lagrangian in the self-interacting O(N) scalar theory, in slowly varying gravitational fields, is presented (using ζ-function regularization and heat-kernel techniques). The result is given in terms of the expansion in powers of the curvature tensors (up to quadratic terms) and their derivatives, as well as in derivatives of the background scalar field (up to second derivatives). The renormalization group improved effective Lagrangian is studied, which gives the leading-log approach of the whole perturbation theory. An analysis of the effective equations (back-reaction problem) on the static hyperbolic spacetime openR2×H2/Γ is carried out for the simplest version of the theory: m2=0 and N=1. The possibility of the existence of the solution openR2×H2/Γ, induced by purely quantum effects, is discussed.

View figure in article

References (62)

  1. E. W. Kolb and M. S. Turner, The Early Universe (Addison Wesley, New York, 1990).
  2. A. D. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic, New York, 1990).
  3. R. H. Brandenberger, Rev. Mod. Phys. 57, 1 (1985).
  4. B. S. DeWitt, The Dynamical Theory of Groups and Fields (Gordon and Breach, New York, 1965).
  5. N. Birrell and P. C. W. Davies, Quantum Fields in Curved Spaces (Cambridge University Press, Cambridge, England, 1982).
  6. I. L. Buchbinder, S. D. Odintsov, and I. L. Shaprio, Effective Action in Quantum Gravity (IOP, Bristol, 1992).
  7. G. M. Shore, Ann. Phys. (N.Y.) 128, 376 (1980).
  8. D. J. O'Connor, B. L. Hu and T. C. Shen, Phys. Lett. 130B, 31 (1983).
  9. B. Allen, Nucl. Phys. B226, 228 (1983).
  10. A. Vilenkin, Nucl. Phys. B226, 504 (1983).
  11. I. L. Buchbinder and S. D. Odintsov, Class. Quantum Grav. 6, 1959 (1989).
  12. D. J. Toms, Phys. Rev. D 26, 2713 (1982).
  13. L. H. Ford and T. Yoshimura, Phys. Lett. 70A, 89 (1979).
  14. L. H. Ford, Phys. Rev. D 21, 933 (1980).
  15. D. J. Toms, Phys. Rev. D 21, 2805 (1980).
  16. L. H. Ford and D. J. Toms, Phys. Rev. D 25, 1510 (1982).
  17. G. Denardo and E. Spallucci, Nuovo Cimento A 58, 243 (1980).
  18. G. Denardo and E. Spallucci, Nucl. Phys. B169, 514 (1980).
  19. A. Actor, Class. Quantum Grav. 7, 663 (1990).
  20. E. Elizalde and A. Romeo, Phys. Lett. B 244, 387 (1990).
  21. E. Elizalde and K. Kirsten, J. Math. Phys. 35, 1260 (1994).
  22. Y. Hosotani, Phys. Rev. D 20, 2783 (1984).
  23. G. Kennedy, Phys. Rev. D 23, 2884 (1981).
  24. G. Cognola, K. Kirsten and S. Zerbini, Phys. Rev. D 48, 790 (1993).
  25. A. A. Bytsenko, K. Kirsten and S. D. Odintsov, Mod. Phys. Lett. A 8, 2011 (1993).
  26. R. Critchley and J. S. Dowker, J. Phys. A 15, 157 (1982).
  27. D. J. O'Connor, B. L. Hu and T. C. Shen, Phys. Rev. D 31, 2401 (1985).
  28. D. J. O'Connor and B. L. Hu, Phys. Rev. D 34, 2535 (1986).
  29. T. Futamase, Phys. Rev. D 29, 2783 (1984).
  30. A. Ringwald, Ann. Phys. 177, 129 (1987).
  31. A. Ringwald, Phys. Rev. D 36, 2598 (1987).
  32. J. B. Hartle and B. L. Hu, Phys. Rev. D 20, 1772 (1979).
  33. A. L. Berkin, Phys. Rev. D 46, 1551 (1992).
  34. I. L. Buchbinder and S. D. Odintsov, Class. Quantum Grav. 2, 721 (1985).
  35. D. J. O'Connor and B. L. Hu, Phys. Rev. D 30, 743 (1984).
  36. R. Critchley, B. L. Hu and A. Stylianopoulos, Phys. Rev. D 35, 510 (1987).
  37. G. Cognola, K. Kirsten and L. Vanzo, Phys. Rev. D 48, 2813 (1993).
  38. C. Wiesendanger and A. Wipf, Ann. Phys. 233, 125 (1994).
  39. G. T. Horowitz and R. M. Wald, Phys. Rev. D 17, 414 (1978).
  40. M. V. Fischetti, J. B. Hartle and B. L. Hu, Phys. Rev. D 20, 1757 (1979).
  41. J. B. Hartle and B. L. Hu, Phys. Rev. D 21, 2756 (1980).
  42. P. Anderson, Phys. Rev. D 28, 271 (1983).
  43. S. W. Hawking, Commun. Math. Phys. 55, 133 (1977).
  44. R. Critchley and J. S. Dowker, Phys. Rev. D 13, 3224 (1976).
  45. L. Parker and D. J. Toms, Phys. Rev. D 31, 953 (1985).
  46. L. Parker and D. J. Toms, Phys. Rev. D 31, 2424 (1985).
  47. I. Jack and L. Parker, Phys. Rev. D 31, 2439 (1985).
  48. R. Utiyama and B. J. DeWitt, Math. Phys. 3, 608 (1962).
  49. S. Coleman and E. J. Weinberg, Phys. Rev. D 7, 1888 (1973).
  50. M. B. Einhorn and D. R. T. Jones, Nucl. Phys. B211, 29 (1983).
  51. G. B. West, Phys. Rev. D. 27, 1402 (1983).
  52. K. Yamagishi, Nucl. Phys. B216, 508 (1983).
  53. M. Sher, Phys. Rep. 179, 274 (1989).
  54. B. Kastening, Phys. Lett. B 283, 287 (1992).
  55. M. Bando, T. Kugo, N. Maekawa and H. Nakano, Prog. Theor. Phys. 90, 405 (1993).
  56. C. Ford, D. R. T. Jones, P. W. Stephenson and M. B. Einhorn, Nucl. Phys. B395, 17 (1993).
  57. E. Elizalde and S. D. Odintsov, Phys. Lett. B 321, 199 (1994).
  58. E. Elizalde and S. D. Odintsov, Phys. Lett. B 303, 240 (1993).
  59. L. Parker and J. Simon, Phys. Rev. D 47, 1339 (1993).
  60. D. A. Hejhal, The Selberg Trace Formula for PSL(2, R) (Springer Verlag, Berlin, 1976), Vols. I and II.
  61. G. F. R. Ellis, Gen. Relativ. Gravit. 2, 7 (1971).
  62. H. V. Fagundes, Phys. Rev. Lett. 70, 1579 (1993).

Outline

Information

Phys. Rev. D 50, 5137– Published 15 October, 1994
  • Received 21 January 1994

© 1994 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation