Relationship of field-theory based single boson exchange potentials to current ones

Abstract

It is shown that field-theory based single boson exchange potentials cannot be identified to those of the Yukawa or Coulomb type that are currently inserted in the Schrödinger equation. The potential which is obtained rather corresponds to this current single boson exchange potential corrected for the probability that the system under consideration is in a two-body component, therefore missing contributions due to the interaction of these two bodies while bosons are exchanged. The role of these contributions, which involve at least two boson exchanges, is examined. The conditions that allow one to recover the usual single boson exchange potential are given. It is shown that the present results have some relation: i) to the failure of the Bethe-Salpeter equation in reproducing the Dirac or Klein-Gordon equations in the limit where one of the constituent has a large mass, ii) to the absence of corrections of relative order alpha log(1/alpha) to a full calculation of the binding energy in the case of neutral massless bosons or iii) to large corrections of wave-functions calculated perturbatively in some light-front approaches.

arXiv commentLaTeX, 37 pages, 14 figures, submitted for publication

Cited by in corpus (5)

• Structures of Rotating Traditional Neutron Stars and Hyperon Stars in the Relativistic $\sigma -\omega$ Model
• Form factors in the "point form" of relativistic quantum mechanics: single and two-particle currents
• From the Bethe-Salpeter equation to non-relativistic approaches with effective two-body interactions
• RQM description of the charge form factor of the pion and its asymptotic behavior
• RQM description of PS meson form factors, constraints from space-time translations, and underlying dynamics