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 $\mathrm{uU}$-separating matrix, in Chraplyvy's sense.

In the nonrelativistic limit expansions in powers of $\frac{1}{m}$ or $\frac{1}{c}$ are made. The approximate wave equations are in agreement with previous transformation results.

• Received 14 April 1958

DOI:https://doi.org/10.1103/PhysRev.111.1011