Foundations of Physics

, Volume 10, Issue 3–4, pp 267–280 | Cite as

A gauge field theory of spacetime based on the de Sitter group

  • P. K. Smrz


A new theory of spacetime is proposed in which translations are considered as a part of the de Sitter gauge group. The theory is built along the general principles of classical gauge field theories, which are outlined. Applications of gauge principles to linear and affine connections are also given in order to make the presentation self-sufficient. A de Sitter invariant Lagrangian is constructed, which yields approximately Einstein's vacuum equations when it is subjected to variation with respect to gauge potentials and the result expressed in a specific gauge class. As a difference from the usual use of de Sitter groups, the radius of its translations must be small in the present approach, which probably has the meaning of an elementary subatomic length. The solution of the equations describing flat spacetime is not the trivial zero-curvature connection of the conventional approach.


Gauge Group General Principle Conventional Approach Present Approach Gauge Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Utiyama,Phys. Rev. 101, 1597 (1956).Google Scholar
  2. 2.
    T. W. B. Kibble,J. Math. Phys. 2, 212 (1961).Google Scholar
  3. 3.
    K. Hayashi,Prog. Theor. Phys. 39, 494 (1968).Google Scholar
  4. 4.
    F. W. Hehl, P. v. d. Heyde, G. D. Kerlick, and J. M. Nester,Rev. Mod. Phys. 48, 393 (1976).Google Scholar
  5. 5.
    P. K. Smrz,J. Austral. Math. Soc. 20B, 38 (1977).Google Scholar
  6. 6.
    C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (Freeman 1973), p. 49.Google Scholar
  7. 7.
    Y. Aharonov and D. Bohm,Phys. Rev. 115, 485 (1959).Google Scholar
  8. 8.
    F. W. Hehl, G. D. Kerlick, and P. v. d. Heyde,Phys. Lett. 63B, 446 (1976).Google Scholar
  9. 9.
    M. P. O'Connor and P. K. Smrz,Austral. J. Phys. 31, 195 (1978).Google Scholar
  10. 10.
    P. K. Smrz,Prog. Theor. Phys. 57, 1771 (1977).Google Scholar
  11. 11.
    G. Arcidiacono,Gen. Rel. Grav. 8, 865 (1977).Google Scholar
  12. 12.
    L. D. Landau and E. M. Lifshitz,The Classical Theory of Fields (Pergamon Press, 1962), p. 315.Google Scholar
  13. 13.
    F. W. Hehl and G. D. Kerlick,Gen. Rel. Grav. 9, 691 (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • P. K. Smrz
    • 1
  1. 1.Department of MathematicsUniversity of NewcastleAustralia

Personalised recommendations