The RPA as a group contraction and the implications for symmetries

Using the concept of group contractions we discuss the implications of the RPA for the dynamical group as well as symmetry groups of finite boson systems. In particular it is shown that if the Hartree-Bose ground state breaks the symmetry, the RPA contracts the symmetry group onto a non-semisimple group which is a symmetry group of the RPA hamiltonian. This group contains all subgroups of the original symmetry group which are not broken by the ground state. The abelian invariant subalgebra of the contracted algebra contains the excitation operators of the spurious modes. (orig.)