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29 March 2024
 
  » arxiv » math-ph/9906016

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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
AffiliationRussian Research Center "Kurchatov Institute"
AbstractWe 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
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