Particle Statistics in Topologically Nontrivial
TwoDimensional Magnetic Systems
Theodore J. Allen #
Department of Physics
Syracuse University, Syracuse, NY 132441130
It is demonstrated that charged particles may acquire unusual statistics in topo
logically nontrivial twodimensional samples placed in strong magnetic fields. These
novel statistics follow from an analysis of the selfadjoint extensions of the Landau
Hamiltonian which are partially classified by the UIR's of the fundamental group.
Superselection rules corresponding to di#erent quantum theories are found. Super
symmetry arguments are used to construct exact ground states.
# Email 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