Coherent state theory of the noncompact symplectic group

Abstract

An extended coherent statetheory is presented for the noncompact Sp(3,R) group which reveals a simple relationship between the Sp(3,R) algebra and its contracted u(3)‐boson limit. The relationship is used to derive a remarkably accurate analytic expression for Sp(3,R) matrix elements for the generic lowest‐weight representations. The expression is shown to be exact whenever the states involved are multiplicity free with respect to the u(3) subalgebra. It is further shown how exact matrix elements are easily calculated in general. Dyson and Holstein–Primakoff type u(3)‐boson expansions are given.