Gauge dependences of the covariant effective action in QED

Abstract

A recent computation of the (nonlocal) covariant effective action of QED in weak constant external electromagnetic fields is generalized to general Lorentz gauges and its gauge dependence is displayed, and it is then removed by the prescription for a gauge and parametrization independent effective action according to Vilkovisky. The geometry, which in this framework is ascribed to the field configuration space of QED, is made explicit, and it is shown that Vilkovisky’s effective action coincides with the conventional Landau gauge case.