QUANTIZED VORTEX MOTION AND THE MOTION OF CHARGED-PARTICLES IN A STRONG MAGNETIC-FIELD

Vortices in a two-dimensional superfluid have been suggested to obey "intermediate" statistics, which in two dimensions interpolate between the boson and fermion cases. But questions have been raised concerning this interpretation and the relation between the vortex description and the underlying microscopic theory. The relation between the point-vortex description and the microscopic theory is examined here, but first in a rather general way, without specifying the detailed dynamics of the underlying theory. A system closely related to the vortex system in the superfluid is then studied. This system consists of charged particles in a strong magnetic field, with a two-dimensional Coulomb interaction between the particles. For this system a vortex description is given, and the statistics parameter is explicitly determined. The vortex system of the two-dimensional superfluid is discussed more briefly at the end of the paper. For this system there are additional complications, and no clear result concerning the statistics parameter of this system is given. © 1990.