Effective Group Structure in the Interacting Boson Model

Spectrum generating algebras are used in various fields of physics as models to determine quantum structure, including energy levels and transition strengths. The advantage of such models is that their group structure allows an extensive understanding of the system being studied. In addition they possess a simple classical limit, at least for bosonic systems. In this paper we discuss an algebraic model of nuclear structure, the Interacting Boson Model (IBM), and show that in one limit its group structure is particularly simple. For zero angular momentum there is an effective lower dimensional group structure which describes the system both classically and quantum mechanically.