The relativistic two-body potentials of constraint theory from summation of Feynman diagrams
arXiv:hep-ph/9602241 · doi:10.1006/aphy.1996.5632
Abstract
The relativistic two-body potentials of constraint theory for systems composed of two spin-0 or two spin-1/2 particles are calculated, in perturbation theory, by means of the Lippmann-Schwinger type equation that relates them to the scattering amplitude. The cases of scalar and vector interactions with massless photons are considered. The two-photon exchange contributions, calculated with covariant propagators,are globally free of spurious infra-red singularities and produce at leading order O(α^4) effects that can be represented in three-dimensional x-space by local potentials proportional to (α/r)^2. Leading contributions of n-photon exchange diagrams produce terms proportional to (α/r)^n. The series of leading contributions are summed. The resulting potentials are functions, in the c.m. frame, of r and of the total energy. Their forms are compatible with Todorov's minimal substitution rules proposed in the quasipotential approach.
60 pages, Latex, with four pages of figures included at the end of the article in a Latex file calling the FEYNMAN macropackage
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