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The relativistic two-body potentials of constraint theory from summation of Feynman diagrams

H. Jallouli·H. Sazdjian
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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.

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H. Jallouli, H. Sazdjian. 1996-02-07. The relativistic two-body potentials of constraint theory from summation of Feynman diagrams. https://doi.org/10.1006/aphy.1996.5632

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