By the same authors

From the same journal

From the same journal

The Lorentz Gauge in Non-Relativistic Quantum Electrodynamics

Research output: Contribution to journalArticle

Author(s)

Department/unit(s)

Publication details

JournalProceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
DatePublished - 8 Oct 1982
Issue number1785
Volume383
Number of pages18
Pages (from-to)485-502
Original languageEnglish

Abstract

It is shown how the conventional Lagrangian of non-relativistic 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 Gupta-Bleuler method. Calculations based on this approach with the use of ordinary perturbation theory for the free-space Lamb-shift 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 non-relativistic theory in the Lorentz gauge is also used to compute the order-$e^2$ 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.

Discover related content

Find related publications, people, projects, datasets and more using interactive charts.

View graph of relations