Bound states in quantum electrodynamics: Theory and application

The basic methods that have been used for describing bound-state quantum electrodynamics are described and critically discussed. These include the external field approximation, the quasi-potential approaches, the effective potential approach, the Bethe-Salpeter method, and the three-dimensional equations of Lepage and other workers. Other methods less frequently used but of some intrinsic interest such as applications of the Duffin-Kemmer equation are also described. A comparison of the strengths and shortcomings of these various approaches is included.