Geometrically formulated gauge dynamics for extended hadrons

Abstract

A de Sitter gauge invariant set of field equations is investigated as a possible basis for a gauge description of extended hadrons. The formalism uses an underlying geometric structure given by a fiber bundle over space-time with Cartan connection possessing as fiber a 4-dimensional space of constant curvature characterized by a curvature radius R chosen to be of the order of a Fermi. The constant R represents an elementary length parameter of geometric origin associated with strong interaction physics. A curvature is induced on the bundle space through a hadronic matter distribution described by a generalized bilocal wave field ψ (x, Ξ) where x denotes a point in the base space (space-time) and Ξ varies in the local fiber. An expansion of the internal motion associated with the variable Ξ is given in terms of “de Sitter plane waves”, i.e. the so-called horospherical waves, which are the analogue of the usual plane waves in flat Minkowski space-time. In this context the harmonic analysis of scalar and spinor fields in (4,1) de Sitter space is discussed and its relevance to the SO(4,1) gauge theory is pointed out.