New isotopic spin space and classification of elementary particles

Abstract

We start from the new idea that isotopic spin space is invariant under the group of three dimensional complex conjugate rotations and justify this assumption on the basis of a classical model of extended particles described by relativistic rotators. We then express in terms of Euler parameters (a relativistic generalization of real three dimensional Euler angles) the infinitesimal operators of the Lie algebra associated with this group and obtain, in the general space of the corresponding eigenfunctions, finite dimensional sub-spaces associated with irreducible representations of the complex rotation group. In each subspace one then readily defines a set of « isotopic » or « internal state vectors » corresponding to different types of elementary particles so that each particle family is connected with an irreducible representation of this group. In this scheme isotopic strangeness and fermionic numbers correspond to certain infinitesimal rotation operators and one justifies (with new qualitative aspects) the empirical Nishijima-Gell-Mann classification of elementary particles.