Abstract
The motion of a quantum particle, constrained to move along a space curve via a confining potential, is governed by a hamiltonian that depends on the geometry of the curve. Adiabatic changes in the shape of the curve are shown to give rise to geometric phases. The effect of the latter on the quantization of the motion of the curve itself can be naturally described by a deformation of the canonical commutation relations, providing an example of a noncommutative effective quantum field theory.
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