K. Scharnhorst: Non-local quantum electrodynamics admits a finitely induced gauge field action. Proceedings of the Royal Society of London A: Mathematical and Physical Sciences 451:1943(1995)571-577 (DOI: 10.1098/rspa.1995.0143, available at the JSTOR site: http://www.jstor.org/stable/52738) [arXiv:hep-th/9311099], Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 452:1949(1996)1503, erratum (DOI: 10.1098/rspa.1996.0078, available at the JSTOR site: http://www.jstor.org/stable/52930). [INSPIRE record]
Abstract: This paper reconsiders a result obtained by Chrétien & 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 [i ∂_{x} a(x) - m b(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 ≠ b admits a finitely induced gauge field action, as the present paper demonstrates.