Foldy-Wouthuysen Transformation. Exact Solution with Generalization to the Two-Particle Problem

The Dirac Hamiltonian for a particle in a nonexplicitly time-dependent field is converted to an even Dirac matrix by means of a single canonical transformation. When the interaction term is an odd Dirac matrix, the transformed Hamiltonian is expressed in a very simple form. An exact transformation is also found for two-particle wave equations of Breit's type. The transformed Hamiltonian is then a uU-separating matrix, in Chraplyvy's sense.In the nonrelativistic limit expansions in powers of 1/m or 1/c are made. The approximate wave equations are in agreement with previous transformation results.