Tensor methods and a unified representation theory of SU₃

Abstract

Starting with irreducible tensors, we develop an explicit construction of orthonormal basic states for an arbitrary unitary irreducible representation (λ, μ) of the group SU₃. A knowledge of the simple properties of the irreducible tensors can then be exploited to obtain a variety of results, which ordinarily require more abstract algebraic methods for their derivation. As illustrative applications, we (i) derive Biedenharn's expressions for the matrix elements of the generators of SU₃, (ii) compute the matrix elements of octet-type operators for the case (λ, μ) → (λ, μ), and (iii) develop an explicit unitary transformation connecting the isospin and the U-spin states in any arbitrary irreducible representation.