We consider the dynamics of a relativistic Dirac particle constrained to move in the interior of a twisted tube by confining boundary conditions, in the approximation that the curvature of the tube is small and slowly varying, In contrast with the nonrelativistic theory, which predicts that a particle's spin does not change as the particle propagates along the tube, we find that the angular momentum eigenstates of a relativistic spin-1/2 particle may behave nontrivially. For example, a particle with its angular momentum initially polarized in the direction of propagation may acquire a nonzero component of angular momentum in the opposite direction on turning through 2#pi# radians.Also the usual nonrelativistic effective potential acquires an additional factor in the relativistic theory.
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