Systems Dominated by Exchange Particles

TL;DR

This paper clarifies the physical nature of new relativistic energy levels in two-body systems with Coulomb interaction, showing they are dominated by exchange particles moving at light speed, which explains their absence in non-relativistic models.

Contribution

It reveals that the additional energy levels predicted by the Bethe-Salpeter equation are dominated by exchange particles, providing a physical interpretation absent in earlier non-relativistic analyses.

Findings

New relativistic levels are dominated by exchange particles.

These states move at the speed of light.

They do not appear in non-relativistic Schrödinger models.

Abstract

As well known, the spectrum of a non-relativistic two-body system interacting by the Coulomb potential is the Balmer series $E_n=\frac{\alpha^2m}{4n^2}$ produced by the Schr\"odinger 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 (Schr\"odinger) framework.