Canonical and path-integral quantizations in theA0=0gauge: Abelian case

Abstract

It is shown that both canonical and path-integral quantizations of an electromagnetic field coupled with point charged particles can be carried out in the ${A}_{0}=0$ gauge by the usual rules without fixing the gauge completely and eliminating the longitudinal degrees of freedom. A Coulomb interaction potential is obtained as an effective potential either by separating the longitudinal-mode variables in the Schr\odinger differential equation or by integrating all longitudinal-mode quantum fluctuations in the Feynman path integral. There is no Faddeev-Popov ghost or infinite gauge volume factor in our path-integral treatment.