Weyl reflections in the unitary symmetry theory of strong interactions

Abstract

Recent work has clearly demonstrated the fact that useful predictions in the Ne'eman, Gell-Mann unitary symmetry theory of strong interactions follow from consideration of invariance under the Weyl reflections (generalized charge symmetry operations) of SU₃. Here we describe a fairly rapid and general algebraic method for obtaining the effect of the Weyl reflections on the basis vectors of an arbitrary irreducible representation (IR) of SU₃. The important feature of the method is that it applies to those basis vectors of the IR, which belong to the nonsimple weights of the IR and which can therefore not be treated by inspection of the weight diagram of the IR. Results are given for certain IR's of SU₃ relevant to the Ne'eman-Gell-Mann theory-the 8, 27 and 35 component IRs (1.1) (2.2) and (4.1) of SU₃.