Intermediate statistics for vortices in superfluid films

A quantization of the classical theory of a two-vortex system in a superfluid film is carried out. This is done by finding the representations of an algebra of observables which respect the fact that the vortices are identical objects. The representations depend on an undetermined parameter \ensuremath{\theta}, which may be interpreted as defining intermediate types of statistics for the vortices. We relate our approach to a previous discussion, where only two values for \ensuremath{\theta} were claimed to be possible.