Effective Coupling Constant in Renormalization Group for the Quantum Electrodynamics

Abstract

Effective coupling constant in quantum electrodynamics is investigated. A pole appears in the effective coupling constant for the space-like momentum if it is calculated by perturbation. The pole can be eliminated by the analytic regularization. For QED the effective coupling constant is written in terms of the scale parameter, $\Lambda$, having the dimension of mass as in the case of QCD. $\Lambda$ is determined by comparing with the experimental data. The calculated result agrees with experiment with $\Lambda\approx 1.64\times 10^{47}$ GeV; it is very large but much smaller than the mass scale of Landau ghost.