Abstract
Electric charges on a circle in the presence of a fractional magnetic flux are considered. A winding operator and a flux operator are defined and the corresponding phase space is shown to describe the global properties of the system. The Heisenberg - Weyl group of discrete displacements and the SL(2,Z(q)) group of discrete Bogoliubov transformations in the s-w phase space, are studied. They describe coherent evolution of the system, going beyond the external field approximation and taking into account the back-reaction of the electric charge on the magnetic flux. When q is the power of a prime, Z(q) is a Galois field and stronger results can be proved.
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