Regular perturbation theory of relativistic corrections: Basic aspects

A perturbation approach to the Dirac equation starting from a pair of the Galilei-invariant four-component Levy-Leblond-type equations [J. M. Levy-Leblond, Commun. Math. Phys. 6, 286 (1967)] for a nonrelativistic electron or positron with spin is formulated. The perturbation expansion is obtained by contour integration of matrix elements of the Dirac resolvent expanded into appropriate power series of nonrelativistic resolvents. The expressions for the low-order energy corrections coincide with the well-known formulas for the Rayleigh-Schrödinger coefficients but with the sums going over both nonrelativistic electron and nonrelativistic positron states. To illustrate the method, all-order calculations are performed in the case of a quasifree particle. © 1996 The American Physical Society.