Spin splitting of relativistic particles in 3D

TL;DR

This paper investigates the behavior of relativistic particles under electric and magnetic fields, focusing on spin splitting and Larmor precession, revealing relativistic effects like motional red/blue shifts and Landau level influences.

Contribution

It provides a comprehensive analysis of spin splitting in relativistic particles, highlighting how relativistic effects alter Larmor frequencies and introduce new bounds and shifts.

Findings

Longitudinal motional red shift of Larmor frequency

Existence of a dynamical upper bound for neutral particles

Landau ladder red shift effect for higher Landau levels

Abstract

The behavior of relativistic particles in an electric and/or magnetic field is considered in the general case when the direction of propagation may differ from the direction of the field. A special attention is paid to the spin splitting and the ensuing Larmor precession frequency of both neutral and charged particles. For both neutral and charged particles, the Larmor frequency shows a longitudinal motional red shift. For a neutral particle, there is a dynamical upper bound, which depends on both the mass and the transverse momentum of the particle; moreover, the transverse motion leads to a blue shift of the Larmor frequency. For a charged particle, the longitudinal motional decrease of the spin splitting is determined by the formation of Landau levels and it has no upper limit. Unlike the nonrelativistic limit, the relativistic spin splitting depends on the Landau levels and decreases for higher Landau levels, thereby signalling the presence of a Landau ladder red shift effect.