An analytic formula for u(3)‐boson matrix elements

The u(3)‐boson Lie algebra is the liquid limit of the symplectic algebra sp(3, R). An analytic formula is given for the u(3)‐boson matrix elements in irreducible unitary representations corresponding to the sp(3, R) discrete series. The formula also applies to the generators of the mathematically isomorphic, but physically different, interacting boson algebra.