We study of the appearance of geometric quantum phases in the dynamics of a neutral particle that possess a permanent magnetic dipole moment in rotating frames in a cosmic string spacetime. The relativistic dynamics of spin-$1/2$ particle in this frame is investigated and we obtain several contributions to relativistic geometric phase due rotation and topology of spacetime. We also study the geometric phase in the nonrelativistic limit. We obtain effects analogous to the Sagnac effect and Mashhoon effect in a rotating frame in the background of a cosmic string.
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Bakke et al. (2009) studied this question.
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