By Herman Feshbach Professor of Physics Frank Wilczek

This selection of articles by means of experts in fractional data levels from describing tricky ordered states of condensed topic - and suggesting new ones - to editing the elemental rules of black gap physics.

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**Extra resources for Fractional Statistics and Anyon Superconductivity**

**Example text**

L. 21 4. Aharonov-Bohm Scattering and Its Implications 1. In this number I will present a self-contained derivation of the scattering cross-section for a charged pa~ticle scattering off an infinitesimal flux tube, as was first calculated by Aharonov and Bohm in a quite different (and rather clumsy) way. The result has important applications in anyon physics, which will be spelled out in the later numbers of this Section. To begin the discussion, let us consider an auxiliary problem that is of some independent interest.

Since the vector potential depends on the particle positions, it varies in time, and one might therefore expect there to be electric fields depending on the relative positions of the particles, and therefore for there to be forces among them. Of course we know from the preceding discussion that it is not so: what gives? Another puzzle is this: how does our H, lacking as it does the standard scalar potential piece, manage to give gauge-invariant results? The resolution of these puzzles is really quite simple.

In other words, when the charge-flux connection arises from a Chern-Simons term, the statistical phase is one-half its nominal value qc) q2 / J-L. S a significant difference between the statistics of ordinary charge/flux tube composites, and that of objects where the charge-flux relation is determined dynamically by the equation of motion of the gauge fieln. The statistics is not determined exclusively by the value of the charge and flux, but depends on their origin as well. 37 5. It is very instructive to pass from the Lagrangian form of the Chern-Simons interaction, discussed so far, to a Hamiltonian form.