Binary Boosts

Abstract

The relativistic motion of an isolated two--body system (bound or unbound) of given lab energy $K^0$ in QED is separated into cms motion and relative motion. The relative motion equation ${\mathcal{K}}_L{\psi }_L({\mathbf{r}}_L)=0$ contains the momentum eigenvalue $\mathbf{K}$ of the cms motion. It is greatly simplified by a binary boost to the atomic rest frame, where $K^0$ and $\mathbf{K}$ appear only in a Lorentz--invariant combination. This boost is not a product of single--particle boosts, which are useful only for perturbative interactions. CPT--invariance is demonstrated, and orthogonality relations are derived.

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