Relativistic bound-state equations for two-fermion systems

Details Relativistic bound-state equations for two-fermion systems Relativistic bound-state equations for two-fermion systems

1999-06-21

arxiv.org/abs/math-ph/9906016v2

Physics

Mathematical Physics

9 pages, 2 figures, RevTeX

Scientific paper

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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