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arXiv:1204.2276 [math.AP]AbstractReferencesReviewsResources

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

Published 2012-04-10, updated 2012-05-24Version 2

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.

Comments: 15 pages, 6 figures. Submitted to Theoretical and Mathematical Physics. v2: A change has been made to the paragraph describing the previous work of M. Prokhorova
Journal: Teoret. Mat. Fiz. 172:3 (2012) 437-453; Theoret. Math. Phys. 172:3 (2012) 1263-1277
Subjects: 58J30, 58J20, 19K56
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