α-Lorentz gauge QED

Abstract

The α-Lorentz gauge is defined as a generalisation of the Lorentz gauge, which contains the Coulomb and usual Lorentz gauges as special cases. A self-consistent formulation of a non-relativistic QED within the α-Lorentz gauge is presented, via the canonical procedure, after the manner of Gupta and Bleuler. This is made possible by the equivalence in the propagation speeds (= αc) of the longitudinal and scalar photons and results in the identification of the usual Lorentz gauge supplementary condition as being also the quantum analogue of the α-Lorentz gauge condition. The Hamiltonian's α dependence is superficial and does not influence observables. This is illustrated by a calculation of the hydrogenic Lamb shift. The conditions under which the scalar potential is capable of entering an electromagnetic interaction are investigated.