• Corpus ID: 118353046

Relativistic bound-state equations for two-fermion systems

@article{Agafonov1999RelativisticBE,
  title={Relativistic bound-state equations for two-fermion systems},
  author={A. I. Agafonov and Eduard A. Manykin},
  journal={arXiv: Mathematical Physics},
  year={1999}
}

• A. Agafonov, E. Manykin
• Published 21 June 1999
• Physics
• arXiv: Mathematical Physics

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.