Mean field theory for usp(4) ≅ so(5)

The simple Lie algebra usp(4) ≅ so(5) is a ten-dimensional algebra that contains the angular momentum algebra su(2). In nuclear structure physics, the algebra so(5) describes beta-rigid collective modes in the Bohr-Mottelson and interacting boson models. The so(5) dual space consists of density matrices which are defined by the expectations of so(5) generators. A coadjoint orbit is a common level surface in the dual space of the two so(5) Casimirs. This paper develops mean field theory on any coadjoint orbit of so(5) densities. When the densities of a set of quantum states lie on one orbit, the system is said to have a weak dynamical symmetry. A Lax pair determines the dynamics of so(5) densities on each coadjoint orbit. Analytic solutions are reported for rotating so(5) densities in equilibrium for a particular energy function