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Relativistic bound-state equations for two-fermion systems | A.I. Agafonov
; E.A. Manykin
; | Date: |
21 Jun 1999 | Subject: | Mathematical Physics | math-ph math.MP | Affiliation: | Russian Research Center "Kurchatov Institute" | 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. | Source: | arXiv, math-ph/9906016 | Services: | Forum | Review | PDF | Favorites |
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