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arXiv · 1204.2276

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

M. I. Katsnelson·V. E. Nazaikinskii
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Abstract

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.

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M. I. Katsnelson, V. E. Nazaikinskii. 2012-04-10. The Aharonov-Bohm effect for massless Dirac fermions and the spectral flow of Dirac type operators with classical boundary conditions. https://doi.org/10.4213/tmf8337

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