Quantum dynamics and statistics of vortices in two-dimensional superfluids

The phase change of the wave function of a superfluid film as a vortex moves around a closed path counts the number of superfluid particles enclosed by that path. This result is used to investigate whether such vortices obey ‘‘fractional statistics.’’ We conclude that this is not the case in compressible superfluids such as ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films.