Eigenvalue boundary problems for the Dirac operator
type: Item
instance of: scholarly article
title: Eigenvalue boundary problems for the Dirac operator
zbMATH Open document ID: 1018.58020
author: Oussama Hijazi
author: Sebastián Montiel
author: A. Roldán
published in: Communications in Mathematical Physics
publication date: 2003-03-27T00:00:00Z
review text: Let \(M\) be a compact Riemannian spin manifold with non-empty boundary. The authors study the spectrum of the Dirac operator under four different boundary conditions: (1) the global Atiyah-Patodi-Singer condition associated with the spectral resolution of the intrinsic boundary Dirac operator, (2) the local condition associated with a chirality operator, (3) MIT bag boundary conditions, and (4) a new global boundary condition that is a modification of the APS condition. The first 3 boundary conditions give rise to self-adjoint realization of the Dirac operator and spectra tending to \(\pm\infty\); the final boundary condition gives rise to a spectra of complex numbers with positive imaginary part. The authors also analyse the classical Friedrich lower bound for the spectrum in terms of scalar curvature provided that the mean curvature of the boundary hypersurface is non-negative.
reviewed by: Peter B. Gilkey
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 1889175
zbMATH Keywords: Atiyah-Patodi-Singer boundary condition
zbMATH Keywords: MIT bag boundary condition
zbMATH Keywords: chirality operator
zbMATH Keywords: Friedrichs inequality
zbMATH Keywords: spectrum
zbMATH Keywords: Dirac operator
MaRDI profile type: Publication
full work available at URL: s00220-002-0725-0
OpenAlex ID: W2011758747
DOI: 10.1007/S00220-002-0725-0
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description: scientific article; zbMATH DE number 1889175