Gauge Dependence of Four-Fermion QED Green Function and a Breakdown of Gauge Invariance in Atom-Like Bound State Calculations

Abstract

We derive a relation between four-fermion QED Green functions of different covariant gauges which defines the gauge dependence completely. We use the derived gauge dependence to check the gauge invariance of atom-like bound state calculations. We find that the existing QED procedure does not provide gauge invariant binding energies. A way to a corrected gauge invariant procedure is pointed out.