Elements of the interacting boson approximation

The main features of the interacting boson model family are briefly summarized. The main tool of the model is the group theory; its basic useful results (symmetry groups, spectrum generating algebra, dynamic groups and symmetries, tensor representations, broken symmetries, subgroup chains) are summarized. The emission and annihilation operators of the individual boson degrees of freedom form a U(n) algebra. Its reprezentation theory can be used to classify the basic states and energy levels of the system. A simple variant of the interacting boson model is analyzed in detail. The genealogy of different interacting boson models from vibron model to supersymmetric ones is surveyed. (D.Gy.)