On the relativistic invariance of QED in the Coulomb gauge and field transformations

Abstract

To establish the relativistic invariance of QED, the equal time commutators (T00(x), T00(x')), (T00(x), T0k(x')) and (T0k(x), T0l(x')) of the energy-momentum tensor density are explicitly worked out in the full theory by making use, in the process, of only the canonical commutation relations of the dynamical independent field components as obtained from the Coulomb gauge. In particular, the equal time commutator (T0k(x), T0l(x')) is shown to be modified (and explicitly worked out) from what one may expect naively with the additional correction term having just the right symmetry property to establish Lorentz covariance. Finally the infinitesimal Lorentz transformations of all the field components are worked out and the consistency of the Coulomb gauge in the new frame is verified.