The dynamical group of the SU(3)-symmetric strong coupling theory

Abstract

Starting from the Hamiltonians, the complete infinite sets of isobaric states for two SU(3)-symmetric strong coupling models (with scalar and pseudoscalar mesons) are determined using the idea of the dynamical group. The physically meaningful unitary irreducible representations of the dynamical groups SU(3) · T 8 and [SU(3) ⊗ SU(2)] · T 24 follow from the minimization requirement on the potential energy part of the Hamiltonians in the strong coupling limit. The composition of these infinite dimensional representations in terms of representations of the symmetry groups SU(3) and SU(3) ⊗ SU(2) has been obtained.