Lie group of the strong-coupling theory. III. Dynamical generation of extra internal symmetry for a class of representations

Abstract

The strong-coupling dynamics, with isospin SU(2)_I as the given internal symmetry group, leads to the generation of a larger internal symmetry group SU(2)_I1⊗SU(2)_I2 (I₁+I₂=I) for the hyperon isobar-pion coupling constants, the hyperon isobar series having isospin-spin I=J±1/2=0, 1, 2, ···, ∞. In this connection we describe a "modified contraction" method for constructing the irreducible representations of the strong-coupling group G=[SU(2)_I⊗SU(2)_J] × T₉, which starts from the "uncontracted" group SU(2)⊗SU(4) and provides a transparent formulation of the dynamical generation of extra symmetry for a class of irreducible representations of group G. One more method for constructing the representations of the group G is also described which starts from a knowledge of the irreducible representations of inhomogeneous Euclidean group in four dimensions.