Dybalski, Wojciech
(2017):
From FaddeevKulish to LSZ. Towards a nonperturbative description of colliding electrons.
In: Nuclear Physics B, Vol. 925: pp. 455469

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Abstract
In a low energy approximation of the massless Yukawa theory (Nelson model) we derive a FaddeevKulish type formula for the scattering matrix of N electrons and reformulate it in LSZ terms. To this end, we perform a decomposition of the infrared finite Dollard modifier into clouds of real and virtual photons, whose infrared divergencies mutually cancel. We point out that in the original work of Faddeev and Kulish the clouds of real photons are omitted, and consequently their waveoperators are illdefined on the Fock space of free electrons. To support our observations, we compare our final LSZ expression for N=1 with a rigorous nonperturbative construction due to Pizzo. While our discussion contains some heuristic steps, they can be formulated as clearcut mathematical conjectures. (C) 2017 The Author. Published by Elsevier B.V.