Many-times formalism and Coulomb interaction

We extend here the many-times formalism, formerly used mainly for particles moving in given classical fields, to interacting particles. In order to minimize the difficulties associated with an equal-time interaction, we limit ourselves to nonrelativistic quantum mechanics and a two-particle interaction, such as that corresponding to the Coulomb force between charged particles. We obtain a set of differential equations which are really not consistent, but they serve as a guide to a formulation in terms of integral equations that has the same perturbation expansion as the usual theory for the scattering of particles. The integral equation for two-particle amplitudes can be modified to give the correct theory for bound states, but this is not the case for more than two particles. We expect that this theory can be generalized to a formulation of relativistic quantum mechanics of interacting particles.