The Low soft-photon theorem again

Abstract

It is shown that contrary to claims of Lebiedowicz et al. (Phys Rev D 105(1):014022, 2022) the formulated in the proper physical variables Low theorem (Low in Phys Rev 110(4):974–977, 1958) for soft photon emission does not require any modification. We also reject the criticism in Lebiedowicz et al. (2022) of the papers (Burnett and Kroll in Phys. Rev. Lett. 20:86–88,1968; Lipatov in Nucl Phys B 307:705–720, 1988). At the same time, we identify some inaccuracies in Burnett and Kroll (1968) in the presentation of the soft-photon theorem for the case of spin-one-half particles. We also point out shortcomings in consideration of the Low theorem in the classic textbooks (Berestetskii et al. in Quantum electrodynamics. Pergamon Press, Oxford, 1982; Lifshitz and Pitaevsky in Relativistic quantum theory, part 2, Fizmatlit, 2002).