Absence of Noncanonical Behavior in Quantum Electrodynamics

Abstract

Using the explicit electromagnetic-field-dependence property of the electromagnetic current according to Schwinger and Johnson, a perturbation-theoretic calculation of equal-time canonical current commutators is carried out to show that there are no noncanonical derivative terms bilinear in the electromagnetic field, contrary to what has been claimed in the past. This result is in accord with that of the Bjorken-Johnson-Low definition for equal-time commutators. It is pointed out that the conventional distribution-theoretic approach to handling singular expressions of field multilinears at the same space-time point fails to take into account field-dependence properties of the kind present in the Schwinger-Johnson ansatz.

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