RECOVERY OF GAUGE-INVARIANCE IN STRONG-COUPLING QED

Under a novel ansatz for the vertex function, the Schwinger-Dyson equation for the fermion propagator in the cutoff QED is solved in the arbitrary gauge, taking account of the vacuum polarization in the photon propagator. For any ultraviolet cutoff A, there exists a bifurcation point e(c)(LAMBDA) of the bare coupling constant above which die trivial fermion-mass function for massless QED bifurcates to another, nontrivial massive solution. With a proper choice of the transverse vertex function and the longitudinal vertex that respects die Ward-Takahashi identity, the critical point e(c)(infinity) and the critical scaling behavior in the vicinity of the critical point are shown to be gauge-independent. In the arbitrary gauge, it is shown that the quenched, planar QED obeys Miransky's scaling of the essential-singularity type and that the unquenched QED exhibits the mean-field critical behavior with classical critical exponents.