Dynamical group chains and integrity bases

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Abstract
An algorithm for constructing a Hamiltonian from the generators of a dynamical group G, which is invariant under the operations of a symmetry group H ⊆ G, is presented. In practice, this algorithm is subject to a large number of simplifications. It is sufficient to construct an integrity basis of H scalars in terms of which all H scalars can be expressed as polynomial functions. In many instances the integrity basis exists in 1–1 correspondence with the Casimir operators for a group–subgroup lattice based on the pair H ⊆ G. When this is so the theory embodies natural symmetry limits and analytic results for observables can be given. Examples of the application of the algorithm are given for the dynamical group SU(2) with symmetry subgroups C3 and U(1) and for SU(N) ⊇ SO(3), N=3, 4, and 6.