A prescription forn-dimensional Vierbeins

  • Ashfaque H. Bokhari
  • Asghar Qadir
Brief Reports

Abstract

Recent developments in supergravity have brought then-dimensional Vierbein formalism into prominence. Here we provide a prescription for writing down a Vierbein given an arbitrary (in general non-diagonal) metric tensor in a Riemannian or pseudo-Riemannian space.

Zusammenfassung

Neuere Entwicklungen in der Supergravitation haben denn-dimensionalen Vierbein in den Vordergrund gerückt. Wir bringen hier einen Vierbein zur Darstellung unter der Voraussetzung eines metrischen Tensors (meist nichtdiagonal) in einem Riemannschen oder pseudo-Riemannschen Raum.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P. van Nieuwenhuizen and D. Z. Freeman,Supergravity (North-Holland, Amsterdam 1979); S. W. Hawking and M. Roček,Supergravity and Superspace (Cambridge University Press, 1981); P. van Nieuwenhuizen, Phys. Rep.68, 192 (1981).Google Scholar
  2. [2]
    W. L. Bade and H. Jehle, Rev. Mod. Phys.25, 714 (1953).Google Scholar
  3. [3]
    D. Brill and J. A. Wheeler, Rev. Mod. Phys.29, 465 (1957).Google Scholar
  4. [4]
    T. L. Curtwright and P. G. O. Freund inSupergravity (Ref. 1); W. Nahm, Nucl. Phys.B135, 149 (1978); See also P. van Nieuwenhuizen in Ref. 1.Google Scholar
  5. [5]
    Th. Kaluza, Sitz. Preuss. Akad. Wiss. Phys. Math. Kl. LIV, 966 (1921); O. Klein, Z. Phys.37, 875 (1926); E. Witten, Search for a realistic Kaluza-Klein theory, Princeton preprint;Google Scholar
  6. [6]
    A. Chodos and S. Detweiler, Phys. Rev.D21, 2167 (1980); L. Halpern,Physics and Contemporary Needs, Vol. 5, Eds. A. Qadir and Riazuddin (Plenum New York, in press); See also Gen. Rel. Grav.8, 623 (1977).Google Scholar
  7. [7]
    In general the solution given by Eq. (18) depends on the path of integration. However, the solution is well-defined if the determinantsD(m), m, n, are non-singular. This is just the requirement given for the prescription to be valid.Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1985

Authors and Affiliations

  • Ashfaque H. Bokhari
    • 1
  • Asghar Qadir
    • 2
    • 3
  1. 1.Mathematics Dept.Quaid-i-Azam UniversityIslamabadPakistan
  2. 2.International Centre for Theoretical PhysicsTriesteItaly
  3. 3.Centre of Basic Sciences (UGC)IslamabadPakistan

Personalised recommendations