Transformation of Relativistic Wave Equations

A unitary transformation is found which transforms the Dirac equation into two uncoupled equations. These involve higher orders of the time derivative than the first. In order (v/c)² the equations involve only the first time derivative and they are then equivalent to the Foldy-Wouthuysen transformation. While the equations are uncoupled and free of odd operators the functions satisfying them cannot be interpreted as different functions describing positive and negative energies separately, the general interpretation in the exact theory remaining in terms of the four-component wave function.The transformation is extended to quantized fields and to relativistic two-body equations. The second-order electromagnetic mass effects in the quantized Dirac equation appear, in the nonrelativistic limit, as the time derivatives of the electric terms of the nonrelativistic Hamiltonian without the radiative corrections. These mass effects in the nonrelativistic Hamiltonian are proportional to (1/mc)³.Construction of unitary transformation operators for the ps-ps meson theory and for the Bethe-Salpeter equation are also discussed.