Anandan quantum phase for a neutral particle with Fermi–Walker reference frame in the cosmic string background

Abstract

We study geometric quantum phases in the relativistic and non-relativistic quantum dynamics of a neutral particle with a permanent
magnetic dipole moment interacting with two distinct field configurations in a cosmic string spacetime. We consider the local
reference frames of the observers are transported via Fermi–Walker transport and study the influence of the non-inertial effects
on the phase shift of the wave function of the neutral particle due to the choice of this local frame. We show that the wave
function of the neutral particle acquires non-dispersive relativistic and non-relativistic quantum geometric phases due to
the topology of the spacetime, the interaction between the magnetic dipole moment with external fields and the spin–rotation
coupling. However, due to the Fermi–Walker reference frame, no phase shift associated to the Sagnac effect appears in the
quantum dynamics of a neutral particle. We show that in the absence of topological defect, the contribution to the quantum
phase due to the spin–rotation coupling is equivalent to the Mashhoon effect in non-relativistic dynamics.