Matrix Elements of the Octet Operator of SU3

Abstract

All the nonvanishing matrix elements of all the components of the tensor operator which belongs to the regular representation (the octet) of SU3 have been evaluated. Of special interest is the component 𝒴, for it is usual in the broken unitary symmetry theory of strong interactions to assume that the interactions which break exact SU3 invariance have the same transformation properties as 𝒴. Previously, matrix elements of 𝒴 connecting states of the same irreducible representation of SU3 have been given by Okubo in the form of the mass formula. Knowledge of all the matrix elements of 𝒴 is essential however if one is to do more than evaluate one-particle matrix elements in the broken unitary symmetry theory. Our method provides such knowledge for all components of the octet tensor operator with little more effort than is needed to treat 𝒴 alone.

Canonically relativistic quantum mechanics: Representations of the unitary semidirect Heisenberg group, U(1,3)⊗sH(1,3)

“…The Little Group may be decomposed into . The general matrix elements for the generators of have been computed by Lurié and MacFarlane [12]. The general expressions result in considerable algebraic complexity when computing the full representations.…”