Anomalous velocity operator in multi-particle Dirac system with electron-electron interaction

Long Huang, Xiaohua Wu, Tao Zhou

Ziro Koba

Soo‐Yong Lee, Hyun‐Woo Lee

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.

B. Obert, S. Takei, W. Metzner

Abstract We analyze the scaling behavior at and near a quantum critical point separating a semimetallic from a superfluid phase. To this end we compute the renormalization group flow for a model of attractively interacting electrons with a linear dispersion around a single Dirac point. We study both ground state and finite temperature properties. In two dimensions, the electrons and the order parameter fluctuations exhibit power‐law scaling with anomalous scaling dimensions. The quasi‐particle weight and the Fermi velocity vanish at the quantum critical point. The order parameter correlation length turns out to be infinite everywhere in the semimetallic ground state.

Rafael Cañete Mesa

In this paper, we study the Zitterbewegung, as the most anomalous and controversial effect of the Dirac equation. For this purpose, we do not establish a study framework, but we carry out a dissection of the Dirac solution for the velocity operator from a wave optics perspective, which will provide us (such as it is) with all the information about the Zitterbewegung, about the true sense and legality of the solution, and of the Dirac equation itself. In particular, we will obtain that said solution of the Dirac equation is composed of two wave packets coupled through the phase functions, and that it is the destructive and constructive confrontation of their group velocities that will give rise to the classical speed of the particle and the quantum anomalous term, respectively. This coupling is the kinetic aspect of a more general energetic development and of a corpuscular etiology, from which we derive a geometry that will then be an active part of any related phenomenology. A geometry will allow us to uncover some primary questions about physical principles, kinetic energy, spin and velocities, as well as differentiate between wave packets, photons and particles.