Abstract
We show that the time evolution of a space curve is associated with a geometric phase. This phase arises from the path dependence of the rotation of the natural Frenet-Serret triad with respect to a nonrotating (Fermi-Walker) frame. We derive a general expression in 1+1 dimension for the phase and the associated gauge potential, and discuss the application of this formalism to the classical, continuous, antiferromagnetic Heisenberg spin chain.
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