Anomalous Velocity Operator in a Multi-Particle Dirac System with Electron-Electron Interactions

Abstract

By examining the multi-particle Dirac system with the regularized Coulomb interaction including the Breit term, we found that there exist anomalous contributions to the velocity exist. Under the Foldy-Wouthuysen transformation, we showed that the effective meanings of the relativistic anomalous effect are spin-orbit coupling and the classical retardation effect in the non-relativistic limit. In this region, even though this result is intuitively appealing, the factor 2 anomaly appears in the term related to the spin-orbit coupling between relativistic and non-relativistic treatments. The reason for this discrepancy and the way to consistency via co-transformation of an operator corresponding to an observable are also discussed.