Fields and algebras of observables in models with superselection rules II. Model with non-Abelian gauge group

The investigation is continued into the field properties of algebraic models in which the physical observables and the superselection rules are determined by gauge groups. A model of a system of fermion fields with non-Abelian gauge group U( 1 ) is considered. The twisting operation is used to prove duality in the Abelian coherent sectors and in the irreducible subspaees of the non-Abelian coherent sectors. Extended intertwining operators that realize the asymptotic unitary equivalence of the coherent sectors are constructed, and normal commutation relations between them are obtained. From them, by means of a Klein transformation, extended intertwining operators that are parafermion fields of second order are constructed.