An Orthogonal Set Constituted by Eight Kinds of Boson Operators

A possible method for obtaining an orthogonal set constituted by eight kinds of boson operators is proposed. The motivation is to apply the set obtained in this paper to three algebras for the study of high temperature superconductivity, i.e., the so(5), the so(4) and the su(2)⊗su(2) algebras. The basic idea here comes from two recent papers by the present authors, one considering a possible method for obtaining an orthogonal set constituted by four kinds of boson operators and one considering the coupling scheme of two su(1,1) spins. The raising and lowering operators for the magnitude of the su(2) spin coupled to two su(2) spins are introduced, and it is found that these operators play an essential role in constructing the set.