Relativistic effects for spin splitting of neutral particles: Upper bound and motional narrowing

TL;DR

This paper investigates relativistic effects on spin splitting in neutral particles with electric and magnetic dipole moments, revealing an upper bound related to rest energy and noninvariance under Lorentz boosts.

Contribution

It introduces the concept of an upper limit for spin splitting and Larmor frequency, and demonstrates their noninvariance under Lorentz transformations, highlighting relativistic effects.

Findings

Spin splitting has an upper bound equal to twice the particle's rest energy.

Larmor precession frequency is similarly bounded and exhibits relativistic effects.

Spin splitting and Larmor frequency are not invariant under Lorentz boosts.

Abstract

We explore the properties of spin splitting for neutral particles possessing electric and magnetic dipole moments propagating in an electromagnetic field. Two notable features of the spin splitting and the associated Larmor precession are found, which are consequences of special relativity. First, we report the existence of an upper limit of spin splitting equal to twice the rest energy of the particle, and a corresponding upper limit for the Larmor precession frequency. Second, we predict the noninvariance of the spin splitting and the corresponding Larmor frequency with respect to Lorentz boosts, which bears resemblance to the classical Doppler effect.