Geometrical representation of interacting boson models: U(3) model
A method is presented by which a geometrical interpretation can be given for boson models without leaving the domain of quantum mechanics. This approach turns out to be particularly useful in symmetry-preserving treatments of deformed boson systems. A U(3) boson model having an SO(2) symmetry, which is to be preserved throughout, is analyzed in detail. For a well-deformed system, rotational and vibrational modes are identified. A procedure is developed by which the parameters of the geometrical description for the deformed case can be calculated in a series expansion controlled by the inverse of the boson number. The method is compared with the corresponding random phase approximation approach. © 1987 The American Physical Society.