De Sitter Structured Connection and Gauge Translations

  • R. R. Aldinger


A local gauge field description of space-time is discussed using fiber bundle techniques as a theoretical framework. The basic idea is to endow ordinary Minkowski space, M4, with a somewhat richer structure than that implied by relativity by attaching to each position x M4 a copy of a four-dimensional micro-space of constant curvature characterized by an elementary subatomic length parameter R of the order of a Fermi, thus allowing for additional internal degrees-of-freedom. Therefore, two sets of variables are introduced: (i) the usual space-time variables x which determine an element of M4 and (ii) a second set ξ which are elements of an internal space F (which is identified with the fiber of a bundle constructed over M4).


Canonical Form Fiber Bundle Minkowski Space Gauge Potential Base Manifold 
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.
    S. Kobayashi and K. Nomizu, “Foundations of Differential Geometry. Vol. 1,” Wiley, New York (1963).Google Scholar
  2. 2.
    W. Drechsler and M. E. Mayer, “Fiber Bundle Techniques in Gauge Theories,” Vol. 6/, Lecture Notes in Physics, Springer-Verlag, Heidelberg (1977).CrossRefGoogle Scholar
  3. 3.
    E. Inönü and E. P. Wigner, On the contraction of groups and their representations, Proc. N.A.S., 39:510 (1953).Google Scholar
  4. 4.
    W. Drechsler, Group contraction in a fiber bundle with a Cartan connection, J. Math. Phys., 18:1358 (1977).Google Scholar
  5. 5.
    R. Utiyama, Invariant theoretical interpretation of interaction, Phys. Rev., 101:1597 (1955).Google Scholar
  6. 6.
    T. W. B. Kibble, Lorentz invariance and the gravitational field, J. Math. Phys. 2:212 (1961).Google Scholar
  7. 7.
    A. Trautman, Fiber bundles associated with space-time, Rep. Math. Phys. 1:29 (1970).Google Scholar
  8. 8.
    P. K. Smrz, A new unified field theory based on de Sitter gauge invariance, Acta Phys. Pol. 10:1025 (1979).Google Scholar
  9. 9.
    R. R. Aldinger, Quantum de Sitter fiber bundle interpretation of hadron extension, Int. J. Theor. Phys. 25:527 (1986).Google Scholar
  10. 10.
    R. R. Aldinger, A. Bohm, P. Kielanowski, M. Loewe, P. Magnollay, N. Mukunda, W. Drechsler and S. R. Komy, Relativistic rotator I: quantum observables and constrained hamiltonian mechanics, Phys. Rev. D 28: 3020 (1983).Google Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • R. R. Aldinger
    • 1
  1. 1.Department of PhysicsEastern Illinois UniversityCharlestonUSA

Personalised recommendations