Abstract
A boson representation of the Hamiltonian is introduced to describe collective motions in nuclei. Two interacting vector bosons differing in their 'pseudospin' projections are used. The non-compact symplectic group Sp(12, R) is the group of dynamical symmetry for the Hamiltonian. If the Hamiltonian satisfies the restriction of preservation of the number of bosons, then in the basis of Sp(12, R) its matrix is block-diagonal with respect to the maximal compact subgroup of Sp(12, R), namely the group U(6). The U(6) structure of the number-preserving Hamiltonian is investigated. The two-boson interaction is expressed in terms of the second-order Casimir operators of the various chains of subgroups of U(6).
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