Studies in perturbation theory. XIV. Treatment of constants of motion, degeneracies and symmetry properties by means of multidimensional partitioning

The multidimensional partitioning technique is reviewed, with particular emphasis on its formal properties. The treatment of constants of motion by this method coincides with a treatment given previously, involving a modified resolvent in the ordinary approach. On the other hand the present method, upon expansion, coincides with Van Vleck's perturbation theory for quasidegenerate states. Bounds and estimates of the remainder related to Padee approximants obtained via inner projections are discussed. The construction of effective-hamiltonians is considered, in particular the energy-independent non self-adjoint ones.