Surface states and chiral symmetry on the lattice.

In a Hamiltonian formalism we study chiral symmetry for lattice fermions formulated in terms of Shockley surface states bound to a wall in an extra spatial dimension. For hadronic physics this provides a natural scheme for taking quark masses to zero without requiring a precise tuning of parameters. We illustrate the chiral anomaly as a flow of states in this extra dimension. We discuss two alternatives for extending the picture to a chiral coupling of gauge fields to such fermions: one with a small explicit breaking of gauge symmetry and one with heavy mirror fermions.