2003/04/21 by G. V. Efimov · 1 citation
Mathematics · Physics and Astronomy · Psychology · #Bethe–Salpeter equation #Mathematical physics #Mathematics #Physics #Psychology #Quantum electrodynamics #Quantum mechanics #advanced mathematical theories #hep-ph
paper · pdf · doi:10.1007/s00601-003-0015-1
published as Few Body Syst. 33 (2003) 199-217
arxiv created 2003/04/21 · openalex publication_date 2003/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a scalar theory: two scalar fields (constituents) with mass m interacting via an exchange of a scalar field (tieon) with mass μ. The BS equation is written in the form of an integral equation in the configuration Euclidean x-space with the kernel which for stable bound states M<2m is a self-adjoint positive operator. The solution of the BS equation is formulated as a variational problem. The nonrelativistic limit of the BS equation is considered. The role of so-called abnormal states is discussed. The analytical form of test functions for which the accuracy of calculations of bound state masses is better than 1% (the comparison with available numerical calculations is done) is determined. These test functions make it possible to calculate analytically vertex functions describing the interaction of bound states with constituents. As a by-product a simple solution of the Wick-Cutkosky model for the case of massless bound states is demonstrated.