N-Dependent Fractional Statistics ofNVortices

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Abstract
A system of N identical point vortices on a plane, e.g., a superfluid-He4 thin film, is studied with use of elementary quantum mechanics. We find the surprising result that the system obeys fractional or θ statistics which depends on N, where θ(N)=πN or πN+π. This result arises from the angular momentum contained in the zero-point motion of the vortices.