Derivation of a quasipotential equation by the Fock–Podolsky method

The Fock–Podolsky (Tamm–Dancoff) method is used to derive a quasipotential equation for the one-time wave ftmction from the equations of quantum electrodynamics. The connection between this equation and the inhomogeneous equation for the four-point Green's function is established. It is shown that although there is no manifest covariance of the expressions for the Green's function in the Coulomb gauge, one can perform a consistent renormalization of the divergent integrals in at least the second order in the charge $e$. It is noted that in this approach one can derive (in a certain approximation) the Breit equation for the fine structure of energy levels.