De Sitter Structured Connection and Gauge Translations
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).
KeywordsCanonical Form Fiber Bundle Minkowski Space Gauge Potential Base Manifold
Unable to display preview. Download preview PDF.
- 1.S. Kobayashi and K. Nomizu, “Foundations of Differential Geometry. Vol. 1,” Wiley, New York (1963).Google Scholar
- 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.W. Drechsler, Group contraction in a fiber bundle with a Cartan connection, J. Math. Phys., 18:1358 (1977).Google Scholar
- 5.R. Utiyama, Invariant theoretical interpretation of interaction, Phys. Rev., 101:1597 (1955).Google Scholar
- 6.T. W. B. Kibble, Lorentz invariance and the gravitational field, J. Math. Phys. 2:212 (1961).Google Scholar
- 7.A. Trautman, Fiber bundles associated with space-time, Rep. Math. Phys. 1:29 (1970).Google Scholar
- 8.P. K. Smrz, A new unified field theory based on de Sitter gauge invariance, Acta Phys. Pol. 10:1025 (1979).Google Scholar
- 9.R. R. Aldinger, Quantum de Sitter fiber bundle interpretation of hadron extension, Int. J. Theor. Phys. 25:527 (1986).Google Scholar
- 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