Systems Dominated by Exchange Particles

As well known, the spectrum of a non-relativistic two-body system interacting by the Coulomb potential is the Balmer series $E_n=\frac{{\alpha }^{2}m}{4n^2}$ produced by the Schrödinger equation. In 1954, Wick and Cutkosky have found, in the Bethe-Salpeter equation framework, that for $\alpha >\frac{\pi }{4}$ the relativistic effects result in new levels (in addition to the Balmer series). However, the physical nature of these new states remained unclear and therefore their existence was being questioned. We have recently shown that these extra states are dominated by the exchange (massless) particles, moving with speed of light. That’s why they did not appear in the non-relativistic (Schrödinger) framework.