Nonlocal QED admits a finitely induced gauge field action

Abstract

The Letter reconsiders a result obtained by Chrétien and Peierls in 1954 within nonlocal QED in 4D [Proc. Roy. Soc. London A 223, 468]. Starting from secondly quantized fermions subject to a nonlocal action with the kernel $[i/{\partial }_{x}a(x)-mb(x)]$ 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 irrespectively of the choice of the nonlocality $a$ $(=b)$. But, the general case $a\ne b$ naturally to be studied admits a finitely induced gauge field action, as the present Letter demonstrates.

10 pages LATEX. Paper also available at http://links.jstor.org/sici?sici=0962-8444%2819951208%29451%3A1943%3C571%3ANQE AAF%3E2.0.CO%3B2-V; erratum at http://links.jstor.org/sici?sici=1364-5021%2819960608%29452%3A1949%3C1503%3AEN QEAA%3E2.0.CO%3B2-K

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