 Neutral Coulomb pair in a uniform magnetic field

For charges $+e,-e$ and relative coordinate $\mathbf{r}={\mathbf{r}}_2-{\mathbf{r}}_1$, total magnetic pseudomomentum is conserved in a uniform magnetic field. In an appropriate symmetric-gauge Lagrangian differing by a total derivative, it is the canonical centre-of-mass momentum. Mechanical centre-of-mass momentum instead equals $\mathbf{K}+e\mathbf{B}\times \mathbf{r}$ and need not be constant. The sector $\mathbf{K}=0$ is not generally a stationary-centre-of-mass frame.