Foundations of Physics

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

Modified Weyl theory and extended elementary objects

  • W. Drechsler


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).


Gauge Theory Symmetry Breaking Homogeneous Space Spinor Wave Curvature Radius 
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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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