A tensor operator is a set of operators that transforms under commutation with the generators of some Lie algebra like an irreducible representation of the algebra. In this chapter, we will define and discuss tensor operators for the SU(2) algebra discussed in chapter 3. A tensor operator transforming under the spin-s representation of SU(2) consists of a set of operators, Oj for f.= 1 to 2s+l (or -s to s), such that ·


It is true, though we have not proved it, that every irreducible representation is finite dimensional and equivalent to one of the representations that we found with the highest weight construction. We can always choose all tensor operators for SU(2) to have this form.