Geometrically formulated gauge dynamics for extended hadrons

  • W. Drechsler
Fiber Bundles and Extended Particle Structures
Part of the Lecture Notes in Physics book series (LNP, volume 94)


A de Sitter gauge invariant set of field equations is investigated as a possible basis for a gauge description of extended hadrons. The formalism uses an underlying geometric structure given by a fiber bundle over space-time with Cartan connection possessing as fiber a 4-dimensional space of constant curvature characterized by a curvature radius R chosen to be of the order of a Fermi. The constant R represents an elementary length parameter of geometric origin associated with strong interaction physics. A curvature is induced on the bundle space through a hadronic matter distribution described by a generalized bilocal wave field ψ (x, Ξ) where x denotes a point in the base space (space-time) and Ξ varies in the local fiber. An expansion of the internal motion associated with the variable Ξ is given in terms of “de Sitter plane waves”, i.e. the so-called horospherical waves, which are the analogue of the usual plane waves in flat Minkowski space-time. In this context the harmonic analysis of scalar and spinor fields in (4,1) de Sitter space is discussed and its relevance to the SO(4,1) gauge theory is pointed out.


Fiber Bundle Constant Curvature Discrete Series Casimir Operator Principal Series 


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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • W. Drechsler
    • 1
  1. 1.Max-Planck-Institut für Physik and AstrophysikMunichGermany

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