Boundary Conditions for Bulk and Edge States in Quantum Hall Systems
  For two dimensional Schroedinger Hamiltonians we formulate boundary conditions that split the Hilbert space according to the chirality of the eigenstates on the boundary. With magnetic fields, and in particular, for Quantum Hall Systems, this splitting corresponds to edge and bulk states. Applications to the integer and fractional Hall effect and some open problems are described. 
E. Akkermans, J. E. Avron, R. Narevich and R. Seiler