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Boundary Value Problems for Dirac Operators on Graphs
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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We carry the index theory for manifolds with boundary of Bär and Ballmann over to first order differential operators on metric graphs. This approach results in a short proof for the index of such operators. Then the self-adjoint extensions and the spectrum of the Dirac operator on the complex line bundle are studied. We also introduce two types of boundary conditions for the Dirac operator, whose spectrum encodes information of the underlying topology of the graph.
Keywords: metric graphs; Dirac operator; boundary value problems 
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     author = {Alberto Richtsfeld},
     title = {Boundary {Value} {Problems} for {Dirac} {Operators} on {Graphs}},
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Alberto Richtsfeld. Boundary Value Problems for Dirac Operators on Graphs. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a21/

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