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Relativistic two-particle treatment enabling quantitative analysis of bound-state formation

Develop a quantitative relativistic analysis for the process in which two free negative kinetic energy particles (for example, a proton and an electron) form a stable positive kinetic energy hydrogen atom via Coulomb attraction, overcoming the absence of a two-particle Dirac equation.

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Background

In discussing the microscopic mechanism by which negative kinetic energy (NKE) particles could combine into a stable positive kinetic energy (PKE) bound system (e.g., a hydrogen atom), the paper performs a low-momentum analysis but points out that a fully relativistic treatment is required for rigor.

The author states that such a quantitative relativistic analysis is impeded by the lack of a two-particle Dirac equation, leading to an explicit inability to complete the calculation.

References

So far, there has not been a two-particle Dirac equation. Therefore, we are unable to make quantitative analysis as in the case of low-momentum motion.

— A physical mechanism of the generation of stable positive kinetic energy systems and a qualitative explanation of the proportions of the four ingredients in the universe (2402.13263 - Wang, 9 Feb 2024) in Section V (A possible mechanics that stable PKE systems form), microscopic case, after Eq. (76)