General Relativity and Gravitation

, Volume 28, Issue 1, pp 87–96 | Cite as

Factorization of topology changing amplitudes in the Regge calculus approach to quantum cosmology

  • Danny Birmingham
Article

Abstract

We study the form of topology changing amplitudes within the Regge calculus approach to four-dimensional gravity. The four-dimensional simplicial complex is chosen to be a cone over the disjoint union of a number of topologically distinct lens spaces. By restricting attention to a simplicial minisuperspace, the analytic properties of the Regge action can be identified explicitly. The classical extrema and convergent steepest descent contours defining these amplitudes are determined, and a factorization property is established. In the cases studied, we find ground state wave functions which predict Lorentzian oscillatory behaviour in the late universe.

Keywords

Wave Function Regge Action Differential Geometry Disjoint Union Simplicial Complex 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Regge, T. (1961).Nuovo Cimento 19, 558.Google Scholar
  2. 2.
    Hartle, J. B. (1989).J. Math. Phys. 30, 452.Google Scholar
  3. 3.
    Hartle, J. B., and Hawking, S. W. (1983).Phys. Rev. D 28, 2960.Google Scholar
  4. 4.
    Birmingham, D. (1995). “Cobordism Effects in the Regge Calculus Approach to Quantum Cosmology.” Preprint, University of Amsterdam, ITFA-95-3, March 1995.Google Scholar
  5. 5.
    Linde, A. (1984).Zh. Eksp. Tear. Fiz. 87, 369; (1984).Sov. Phys. JETP 60, 211; (1984).Nuovo Cimento 39, 401; (1984).Rep. Prog. Phys. 47, 925.Google Scholar
  6. 6.
    Vilenkin, A. (1984).Phys. Rev. D 30, 509; (1986).Phys. Rev. D33, 3360; (1988).Phys. Rev. D 37, 888.Google Scholar
  7. 7.
    Hartle, J. B., and Sorkin, R. (1981).Gen. Rel. Grav. 13, 541.Google Scholar
  8. 8.
    Brehm, U., and Swiatkowski, J. (1993). “Triangulations of Lens Spaces with Few Simplices.” Preprint, T.U. Berlin.Google Scholar
  9. 9.
    Munkres, J. (1984).Elements of Algebraic Topology (Addison-Wesley, Menlo Park).Google Scholar
  10. 10.
    Rourke, C. P., and Sanderson, B. J. (1972).Introduction to Piecewise Linear Topology (Springer-Verlag, Berlin).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Danny Birmingham
    • 1
  1. 1.Instituut voor Theoretische FysicaUniversiteit van AmsterdamXE AmsterdamThe Netherlands

Personalised recommendations