Group theoretical treatments of strongly correlated atomic dynamics

A revival has occurred in the past fifteen years, connected with the emergence of two challenging problems of atomic dynamics. One deals with high doubly excited states of atoms in which two slow electrons move in a Coulomb field. The second is the study of highly excited states of a single electron in a magnetic field. Both involve non-separable Hamiltonians and competing interactions that are not perturbative. Thereby, analysis through conventional single-particle bases requires the mixing of a diverging number of angular and radial configurations. This has motivated a search for quasi-good symmetries that may provide alternative bases and alternative quantum numbers. Group theoretical analysis, involving primarily variants of O4, has been largely successful in the program regarding angular mixings in both problems. The author gives a unified review of this work, pointing out also what remains to be done, particularly regarding radial correlations which have seen essentially no progress. Links are provided throughout between the group theoretical work and other approaches to these problems