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In a low energy approximation of the massless Yukawa theory (Nelson model) we derive a Faddeev-Kulish type formula for the scattering matrix of $N$ electrons and reformulate it in LSZ terms.
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W. Dybalski and A. Pizzo. Coulomb scattering in the massless Nelson model I. Foundations of two-electron scattering. J. Stat. Phys. 154
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B. Gabai and A. Sever. Large gauge symmetries and asymptotic states in QED . JHEP 12
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