Lamm, Valluri, Jentschura and Weniger comment on"A Convergent Series for the QED Effective Action"by Cho and Pak [Phys. Rev. Lett. vol. 86, pp. 1947-1950 (2001)]

In a recent letter, Cho and Pak claim to have found an additional contribution to the quantum electrodynamic one-loop effective action: a “logarithmic correction term” [see the final result in Eq. (2) and the remark in Ref. [9] of [1]]. However, the “logarithmic correction term” found by Cho and Pak vanishes when the final result is written in terms of the finite, renormalized, physical electron charge. Because current determinations of fundamental constants [2] rely on renormalized QED perturbation theory – without “logarithmic correction terms” of the kind advocated by Cho and Pak –, it is of prime general interest to point out that these terms do not appear if onmass shell renormalization is used. In the on-mass shell scheme, the renormalized QED effective Lagrangian (see e.g. [3, Eq. (3.43)]) reads