Gauge dependence of the effective potential for bilocal composite fields in Abelian gauge theories

The Nielsen-Fukuda-Kugo identity expressing the gauge dependence of effective potentials is generalized to the case of the effective potential for bilocal composite fields in quantum electrodynamics. The resulting identity serves to show the gauge independence of the ground-state energy in the presence of dynamical chiral-symmetry breaking. As a by-product we derive a formula giving the gauge dependence of fermion propagators. It is shown explicitly that the effective potential in the quenched planar approximation does not respect the identity. The Nielsen-Fukuda-Kugo identity is also derived for the effective potential in the auxiliary-field approach