Non-Local Quantum Electrodynamics Admits a Finitely Induced Gauge Field Action

This paper reconsiders a result obtained by Chretien & Peierls within non-local quantum electrodynamics in four dimensions (1954, Proc. R. Soc. Lond. A 223, 468). Starting from secondly quantized fermions, subject to a non-local action with the kernel [Note: See the image of page 571 for this formatted text] [ipartial _xa(x) - mb(x)] and gauge covariantly coupled to an external U(1) gauge field, they found that, for a = b, the induced gauge field action cannot be made finite, irrespective of the choice of the non-locality a (= b). But, the general case studied a neq b admits a finitely induced gauge field action, as the present paper demonstrates.