The paper starts the program of rewriting quantum electrodynamics in terms of the manifestly covariant and covariantly computed effective action. A general method for obtaining nonlocal terms in the effective action is proposed and the term responsible for the one-loop magnetic moment of the electron is worked out. In contrast to the usual calculation based on Green’s functions, the present calculation nowhere encounters the infrared divergences (including renormalization and restriction to the physical mass shell). Comparison with the method of Green’s functions shows the inadequacy of the latter.

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