Degenerate perturbation theory

A number of different perturbation formulations found in the literature are discussed. Although these formulations are derived in quite different ways, simple relations among these derivations are described and, in fact, some are shown to yield identical results. One of these degenerate perturbation theories resulting from different formulations due to Van Vleck, Kemble, and Primas, to des Cloizeaux, and to Buleavski is considered in greater detail. Its linked and cluster expansion properties and some other resummation techniques are briefly discussed.