Abelian Landau-Pomeranchuk-Migdal effects

It is shown that the high-energy expansion of the scattering amplitude calc ulated from Feynman diagrams factorizes in such a way that it can be reduce d to the eikonalized form up to the terms of inverse power in energy in acc ordance with results obtained by solving the Klein-Gordon equation. Therefo re the two approaches when applied to the suppression of the emission of So ft photons by fast charged particles in dense matter should give rise to th e same results. A particular limit of thin targets is briefly discussed, an d it is shown that the correction to the Bethe-Heitler regime is determined by the ratio of the target thickness to the mean free path. If the same is true in QCD, the nuclear LPM effect could be noticeable.