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Relativistic bound-state equations for two-fermion systems

A. I. Agafonov·E. A. Manykin
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Abstract

We point out that the free single-fermion propagator which is used in the QFT equations for two-fermion systems, has a bosonic structure, transforms to the single-boson propagator for the Klein-Gordon equation in the nonrelativistic limit, and, therefore, does not satisfy the Lehmann spectral representation for fermions. Proceeding from the Lippmann-Schwinger integral equation, we obtain a two-fermion relativistic wave equation in which the free two-fermion equal-time propagator satisfying the Lehmann representation, is used. This wave equation has been applied to the electron-positron system. In addition to the eigenstates for positronium, we find a solution which describes a deep bound state with the binding energy $\simeq 2m$ and anomalously small mass of the bound system.

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A. I. Agafonov, E. A. Manykin. 2011-12-09. Relativistic bound-state equations for two-fermion systems. https://arxiv.org/abs/math-ph/9906016

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