Symplectic models of n-particle systems

The dynamical group Sp(6n, R) is used to give a description of the states for n-noninteracting particles confined by an isotropic three-dimensional harmonic oscillator potential. The subgroup structure of the dynamical group is used to determine the relevant spins and unitary group representations of the n-particle states. This is a necessary precursor to developing model Hamiltonians for describing systems such as quantum dots and nuclei in terms of polynomials in the dynamical group generators.