On the theory of collective motion in nuclei. I. Classical theory

From the assumption that the collective Hamiltonian be invariant under the orthogonal group O(A ? 1, $\text{R}$) it is concluded that classical collective dynamics can be formulated on a symplectic manifold. This manifold is shown to be a coset space of the symplectic group $\text{L}$h(6, $\text{R}$) of dimension 12, 16 or 18. The first case corresponds to the dequantization of closed-shell collective dynamics and is described in terms of six complex s- and d-quasiparticles. In the limit A ? 1 it is shown that a transformation leads to interacting s- and d-bosons with the symmetry group $\text{u}$ (6) in the collective phase space.