Abstract
We show that the change of the phase of any quantum state evolving cyclically under the action of the Poincaré or Galilei group is described by a natural affine connection on the symmetry group and by a projective unitary representation of that group. In the special case of a massive particle with spin in a rotating magnetic field and also in the case of photon passing through a helically wound optical fibre, our method reproduces the formulae calculated by Berry and by Chiao and Wu, respectively. Thus the relativistic and nonrelativistic approaches are considered simultaneously and we acquire a more general view of the origin of Berry's phase in quantum systems.
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