Nonlocal regularizations of gauge theories

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Abstract

A procedure is given for generalizing local, gauge-invariant field theories to nonlocal ones which are finite, Poincar\'e invariant, and perturbatively unitary. These theories are endowed with nonlocal gauge symmetries which ensure current conservation and decoupling in the same way that their local analogs do in the parent theories. An elegant way of viewing the resulting on-shell symmetry transformations is as ``quantum representations'' of the local gauge group in which the representation matrices become field-dependent, nonlocal operators. By varying the scale of nonlocality one can obtain gauge-invariant regularization schemes which are manifestly Poincar\'e invariant, perturbatively unitary, and free of automatic subtractions. Since our method does not entail changing either the particle content or the dimension of spacetime, it may preserve global supersymmetry. As applications we work out the electron self-energy and vacuum polarization in QED at one loop. The latter gives the surprising result that no Landau ghost occurs with the regulator on and before renormalization. Another surprise is the absence of an axial-vector anomaly.

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