Gauge-independent bifurcation to the chiral-symmetry-breaking solution of the Dyson-Schwinger equation in continuum QED

The Dyson-Schwinger equation for the fermion propagator can be effectively solved in the approximation of the small-momentum-transfer vertex function. There exists a critical value of the coupling constant above which the ordinary infrared-divergent solution for massless quantum electrodynamics bifurcates to another, massive solution. With a proper transverse part included in the vertex function, the bifurcation point is gauge independent, the new solution is finite in all gauges, and does not require momentum cutoffs of any kind.