Locally gauge-invariant charged states in quantum electrodynamics

Abstract

In a covariant formulation of spinor electrodynamics a la Hertz it is possible to introduce electrically charged matter fields and a vector potential which are invariant under local gauge transformations (characterized by functions vanishing at infinity). The connected Green’s functions relative to such fields turn out to not depend on the gaugefixing parameter and coincide with the corresponding Green’s functions of usual quantum electrodynamics, evaluated in the Landau (fourdimensional transversal) gauge. The states obtained by applying these fields on the vacuum are, however, nonphysical,i.e. Maxwell equations are not weakly satisfied on them. In other words, in the Hertz formulation of quantum electrodynamics local gauge invariance does not imply physicity. Also explicit examples are given of locally gauge-invariant charged physical fields, which are nonlocal with respect to the electromagnetic field.