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

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.