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

Autor:	Katsnelson, M. I., Nazaikinskii, V. E.
Rok vydání:	2012
Předmět:	Mathematics - Analysis of PDEs Condensed Matter - Mesoscale and Nanoscale Physics High Energy Physics - Theory Mathematics - Spectral Theory 58J30 (Primary) 58J20 19K56 (Secondary)
Zdroj:	Teoret. Mat. Fiz. 172:3 (2012) 437-453; Theoret. Math. Phys. 172:3 (2012) 1263-1277
Druh dokumentu:	Working Paper
DOI:	10.4213/tmf8337
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1204.2276 Zobrazit plný text záznamu View this record from Arxiv