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Gauge-theoretical foundation of color geometrodynamics

  • Eckehard W. Mielke
2. Gauge Theories
Part of the Lecture Notes in Physics book series (LNP, volume 139)

Abstract

Salam's SL(6,ℂ) gauge theory of strong interactions is generalized to one having GL(2f,ℂ) ⊗ GL(2c,ℂ or the affine extension thereof as structure group. The concept of fibre bundles and Lie-algebra-valued differential forms are employed in order to exhibit the geometrical structure of this gauge-model. Its dynamics is founded on a gauge-invariant Einstein-Dirac-type Lagrangian. The Heisenberg-Pauli-Weyl non-linear spinor equation generalized to a curved space-time of hadronic dimensions and Einstein-type field equations for the strong f-metric are then derived from variational principles. It is shown that the nonlinear terms are induced into the Dirac equation by Cartan's geometrical notion of torsion. It may be speculated that in this geometrical model extended particles are represented by f x c quarks which are (partially) Confined within geon-like objects.

Keywords

Gauge Theory Gauge Group Bianchi Identity Spinor Field Spinor Equation 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Eckehard W. Mielke
    • 1
  1. 1.Institut für Reine und Angewandte Kernphysik der Christian-Albrecht-Universität KielKiel 1Germany

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