Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities

For a family of self-adjoint Dirac operators - i c ( α · ∇ ) + c 2 2 subject to generalized MIT bag boundary conditions on domains in R 3 , it is shown that the nonrelativistic limit in the norm resolvent sense is the Dirichlet Laplacian. This allows to transfer spectral geometry results for Dirichl...

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Published inMathematical physics, analysis, and geometry Vol. 27; no. 3; p. 12
Main Authors Behrndt, Jussi, Frymark, Dale, Holzmann, Markus, Stelzer-Landauer, Christian
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.09.2024
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Boundary conditions
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Operators
Physics
Physics and Astronomy
Theoretical
Secondary: 35Q40
Spectral inequalities
Generalized MIT bag boundary conditions
Nonrelativistic limit
58J50
Dirac operator
Primary: 81Q10
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Summary:For a family of self-adjoint Dirac operators - i c ( α · ∇ ) + c 2 2 subject to generalized MIT bag boundary conditions on domains in R 3 , it is shown that the nonrelativistic limit in the norm resolvent sense is the Dirichlet Laplacian. This allows to transfer spectral geometry results for Dirichlet Laplacians to Dirac operators for large c .
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ISSN:1385-0172
1572-9656
1572-9656
DOI:10.1007/s11040-024-09484-x