Abstract
Abstract The perturbation theory of relativistic effects is outlined, with the stress on direct perturbation theory(DPT), which is free from the singularities that plague approaches based on the Foldy-Wouthuysen transformation. The nonrelativistic limit (nrl) of the Dirac equation consistent with DPT is the Levy-Leblond equation, which has to be combined with the nrl of electrodynamics. If one cannot solve the Schrodinger equation or the inhomogeneous differential equations of DPT exactly, the method of choice is stationary direct perturbation theory. The leading correction to the wave function is then obtained by making the Hylleraas-Rutkowski functional stationary. This functional has a nice minimax property. If one cares for a regular approximation (the exact relativistic corrections to the wave function have ln r-type singularities near a nucleus) it is important to regularize the upper and the lower component of the bispinor consistently. Quasidegenerate DPT is the generalization to the case where a degeneracy or near-degeneracy in the nrl is split by relativity. The last part of this chapter is devoted to many-electron systems, both at the Hartree-Fock level and with inclusion of electron correlation. Also various fundamental problems of relativistic many-electron Hamiltonians are discussed. DPT is free from variational collapse and unaffected by the Brown-Ravenhall disease.
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