Problems with the filling factor in the quantum Hall effect

Abstract

Already in elementary quantum mechanics on the T n inequivalent representations exist and one has to use reducible representations to implement some automorphisms unitarily. A special example is the quantum Hall system on the T 2. There exists a preferable representation for all B but in the passage to several particles the Pauli principle can be formulated in a physically satisfying way only if the commutant is abelian, i.e. for integer magnetic monopoles.