Nonlocal QED admits a finitely induced gauge field action

TL;DR

This paper revisits a 1954 result in nonlocal QED, showing that a finitely induced gauge field action is possible when the nonlocal kernels differ, expanding understanding of nonlocal gauge theories.

Contribution

It demonstrates that in nonlocal QED, a finite induced gauge field action can be achieved when the nonlocal kernels are not equal, extending previous results.

Findings

Finitely induced gauge field action is possible with $a eq b$

The case $a = b$ leads to non-finite gauge actions

Revisits and extends classical nonlocal QED results

Abstract

The Letter reconsiders a result obtained by Chr\'etien 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 $[ i\not\partial_x a(x) - m b(x)]$ 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 irrespectively of the choice of the nonlocality $a$ $(= b)$. But, the general case $a \neq b$ naturally to be studied admits a finitely induced gauge field action, as the present Letter demonstrates.