Ladder Schwinger-Dyson Equation and Effective Potential of QED for Arbitrary Covariant Gauges

Abstract

Gauge dependence of the chiral symmetry breaking solutions to the Ladder Schwinger-Dyson equation of QED is investigated analytically and numerically. We found bounds on wave function renormalization and critical coupling for chiral symmetry breaking. Energy of the chiral symmetry breaking vacuum is lower than that of trivial one (for the gauge parameter α> -3). Critical couplings, anomalous dimension and vacuum energies are strongly gauge dependent.