Pseudomomentum conservation for one-body and two-body relativistic dynamics in a constant electromagnetic field

Abstract

The pseudomomentum is conserved for a single charge in any constant (over space and time) electromagnetic field. It is also conserved for a neutral two-body system, not only in a pure (constant) magnetic field, but also in a pure (constant) electric field, and explicit wave equations can be written. A neutral two-body system in a constant electric field is treated in a way that parallels our previous approach to this system in a constant magnetic field. Relative motion is separated, but the relative time now survives, whereas a spacelike degree of freedom gets eliminated. In other cases, there is, in general, no evidence of a closed form of the wave equations, but conservation of the pseudomomentum can be required as a reasonable condition for implicitly determining the so-called ``three-body terms'' in the wave equation.