Fractional Statistics of the Vortex in Two-Dimensional Superfluids

The quantum behavior of two identical point vortices (e.g., in a superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ thin film) is studied. It is argued that this system obeys neither Bose nor Fermi statistics, but intermediate or $\theta$ statistics: We find that a single vortex in this system possesses quarter-fractional statistics (i.e., $\theta =\frac{\pi }{2} or 3\frac{\pi }{2}$). The source of the $\theta$ statistics is identified in the relative zero-point motion of the vortices.