Particle Statistics in Topologically Nontrivial
Two-Dimensional Magnetic Systems
Theodore J. Allen
Department of Physics
Syracuse University, Syracuse, NY 13244-1130
It is demonstrated that charged particles may acquire unusual statistics in topo-
logically nontrivial two-dimensional samples placed in strong magnetic fields. These
novel statistics follow from an analysis of the self-adjoint extensions of the Landau
Hamiltonian which are partially classified by the UIR's of the fundamental group.
Superselection rules corresponding to different quantum theories are found. Super-
symmetry arguments are used to construct exact ground states.
E-mail address: tjallen@suhep, @suhep.phy.syr.edu
Electrons, the most prosaic of particles, are fermions as chemistry amply teaches
us. In dimensions higher than two, only the usual Fermi and Bose and the exotic
parastatistics, which seem to be unrealized in nature, are possible statistics for par-