Geometrical SO(4, 1) gauge theory as a basis of extended relativistic objects for hadrons

Abstract

The geometrical structure for a collective model description of extended relativistic single hadron systems is investigated by considering a Yang-Mills theory of the de Sitter group SO(4, 1). The full SO(4, 1) symmetry is broken down to that of its SO(3, 1) stability subgroup resulting in a set of Goldstone fields which are taken to represent coordinates of a point in the de Sitter fibre space and are used, along with the original linear gauge fields, to define the vierbein and spin connection on the restricted bundle: P'(M4, SO(3, 1)) contained in/implied by P(M4, SO(4, 1)). The symmetry breaking parameter is taken as a fundamental length relevant to hadron physics. The original linear gauge fields generate a type of parallel transport which is the curved space analogue of development into the flat affine tangent space and serves as the bridge between the geometrical and purely gauge-theoretic descriptions. Upon quantisation, the generator of development in the unitary gauge (Higgs mechanism), for a special class of horizontal Lorentz cross sections, goes over into the de Sitter space momentum which serves to break the mass-spin degeneracy inherent in the Poincare group description and supplies a curved space perturbation in the resulting relativistic Hamiltonian. The Hamiltonian is used to determine a completely solvable set of dynamical equations of motion resulting in the Zitterbewegung of the extended relativistic object.