The Symmetry Group of the Vector and Axial Vector Currents

Abstract

We apply, with a slight modification, the theory proposed earlier [M. Gell-Mann, Phys. Rev. 125, 1067 (1962)] of a higher broken symmetry than the eightfold way. The integrals of the time components of the vector and axial vector current octets are assumed to generate, under equal time commutation, the algebra of SU(3) x SU(3). The energy density of the strong interactions is assumed to consist of a piece invariant under the algebra, a piece that violates conservation of the axial vector currents only and belongs to the representations (3, 3^*) and (3^*, 3), and a piece that violates the eightfold way and belongs to (1, 8) and (8, 1). An attempt is made to assign particles approximately to super-supermultiplets.