The Lorentz Gauge in NonRelativistic Quantum Electrodynamics
Abstract
It is shown how the conventional Lagrangian of nonrelativistic electrodynamics leads to a theory in the Lorentz gauge where the scalar potential is treated on an equal footing with the transverse and longitudinal components of the vector potential. This requires the introduction of an indefinite metric as in the GuptaBleuler method. Calculations based on this approach with the use of ordinary perturbation theory for the freespace Lambshift of hydrogen are shown to exhibit remarkable exact cancellations between parts of the contribution arising from the scalar field and the entire contribution from the longitudinal field to order e^2, and the result is in agreement with Bethe's expression where only transverse photons are involved. The nonrelativistic theory in the Lorentz gauge is also used to compute the ordere^2 potential on a charged particle outside a conductor where again similar exact cancellations are exhibited. The advantage of the formalism in the Lorentz gauge is emphasized in that it provides an unambiguous procedure for the evaluation of the leading Coulomb energy shifts particularly in the interaction of particles with the surfaces of active media where the Coulomb gauge may be problematical.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 October 1982
 DOI:
 10.1098/rspa.1982.0144
 Bibcode:
 1982RSPSA.383..485B