QED in the exact renormalization group

Abstract

The functional flow equation and the quantum master equation are consistently solved in perturbation for chiral symmetric QED with and without four-fermi interactions. Due to the presence of a momentum cutoff, unconventional features related to gauge symmetry are observed even in our perturbative results. In the absence of the four-fermi couplings, a one-loop calculation gives us the standard results of anomalous dimensions and the beta function for the gauge coupling, and therefore the Ward identity, Z₁ = Z₂. This is a consequence of the regularization-scheme independence in the one-loop computation. We also find a photon mass term. When included, four-fermi couplings contribute to the beta function and the Ward identity is also modified, Z₁ ≠ Z₂, due to a term proportional to the photon mass multiplied by the four-fermi couplings.