1204.2276 (M. I. Katsnelson et al.)

The Aharonov-Bohm effect for massless Dirac fermions and the spectral
flow of Dirac type operators with classical boundary conditions    [PDF]

M. I. Katsnelson, V. E. Nazaikinskii

We compute, in topological terms, the spectral flow of an arbitrary family of self-adjoint Dirac type operators with classical (local) boundary conditions on a compact Riemannian manifold with boundary under the assumption that the initial and terminal operators of the family are conjugate by a bundle automorphism. This result is used to study conditions for the existence of nonzero spectral flow of a family of self-adjoint Dirac type operators with local boundary conditions in a two-dimensional domain with nontrivial topology. Possible physical realizations of nonzero spectral flow are discussed.

View original: http://arxiv.org/abs/1204.2276