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Gauge-theoretical foundation of color geometrodynamics

  • 2. Gauge Theories
  • Conference paper
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Differential Geometric Methods in Mathematical Physics

Part of the book series: Lecture Notes in Physics ((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.

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Authors and Affiliations

  1. Institut für Reine und Angewandte Kernphysik der Christian-Albrecht-Universität Kiel, Olshausenstraße 40–60, 2300, Kiel 1, Germany

    Eckehard W. Mielke

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  1. Eckehard W. Mielke
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Heinz-Dietrich Doebner

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© 1981 Springer-Verlag

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Mielke, E.W. (1981). Gauge-theoretical foundation of color geometrodynamics. In: Doebner, HD. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Physics, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10578-6_27

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  • DOI: https://doi.org/10.1007/3-540-10578-6_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10578-7

  • Online ISBN: 978-3-540-38573-8

  • eBook Packages: Springer Book Archive

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