Modified Weyl theory and extended elementary objects

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).