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Foundations of Physics

, Volume 19, Issue 12, pp 1479–1497 | Cite as

Modified Weyl theory and extended elementary objects

  • W. Drechsler
Article

Abstract

To represent extension of objects in particle physics, a modified Weyl theory is used by gauging the curvature radius of the local fibers in a soldered bundle over space-time possessing a homogeneous space G/H of the (4, 1)-de Sitter group G as fiber. Objects with extension determined by a fundamental length parameter R0 appear as islands D(i) in space-time characterized by a geometry of the Cartan-Weyl type (i.e., involving torsion and modified Weyl degrees of freedom). Farther away from the domains D(i), space-time is identified with the pseudo-Riemannian space of general relativity. Extension and symmetry breaking are described by a set of additional fields (\((\tilde \xi ^a (x),R(x)) \in {G \mathord{\left/ {\vphantom {G H}} \right. \kern-\nulldelimiterspace} H}x R^ +\), given as a section on an associated bundle\(\tilde E(B,{G \mathord{\left/ {\vphantom {G H}} \right. \kern-\nulldelimiterspace} H}x R^ + ,\tilde G)\) over space-time B with structural group\(\tilde G\) = G ⊗ D(1), where D(1) is the dilation group. Field equations for the quantities defining the underlying bundle geometry and for the fields\(\tilde \xi ^a (x)\) are established involving matter source currents derived from a generalized spinor wave function. Einstein's equations for the metric are regarded as the part of the\(\tilde G\)-gauge theory related to the Lorentz subgroup H of G exhibiting thereby the broken nature of the\(\tilde G\)-symmetry for regions outside the domains D(i).

Keywords

Gauge Theory Symmetry Breaking Homogeneous Space Spinor Wave Curvature Radius 
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.

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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • W. Drechsler
    • 1
  1. 1.Max-Planck-Institut für Physik und Astrophysik, Werner-Heisenberg-Institut für PhysikMunichFederal Republic of Germany

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