An isoperimetric-type inequality for electrostatic shell interactions for Dirac operators

DOI10.1007/s00220-015-2481-yzbMath1341.81023arXiv1504.04220OpenAlexW3098018402MaRDI QIDQ291955

Luis Vega, Naiara Arrizabalaga, Albert Mas

Publication date: 10 June 2016

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.04220

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Isoperimetric problems for polytopes (52B60)

Related Items (19)

Dirac–Coulomb operators with infinite mass boundary conditions in sectors ⋮ Spectral analysis of Dirac operators with delta interactions supported on the boundaries of rough domains ⋮ Spectral properties of the Dirac operator coupled with \(\delta\)-shell interactions ⋮ Dirac operators with Lorentz scalar shell interactions ⋮ Self-adjointness of the 2D Dirac operator with singular interactions supported on star graphs ⋮ Two-dimensional Dirac operators with singular interactions supported on closed curves ⋮ Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions ⋮ Self-adjoint Dirac operators on domains in \(\mathbb{R}^3\) ⋮ Limiting absorption principle and scattering matrix for Dirac operators with δ-shell interactions ⋮ On the spectral properties of Dirac operators with electrostatic \(\delta\)-shell interactions ⋮ Self‐adjointness for the MIT bag model on an unbounded cone ⋮ General \(\delta\)-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation ⋮ Dirac operators, shell interactions, and discontinuous gauge functions across the boundary ⋮ Eigenvalue curves for generalized MIT bag models ⋮ Leaky quantum structures ⋮ Spectral optimization for strongly singular Schrödinger operators with a star-shaped interaction ⋮ A spectral isoperimetric inequality for cones ⋮ Self-adjointness of two-dimensional Dirac operators on corner domains ⋮ On Dirac operators in \(\mathbb{R}^3\) with electrostatic and Lorentz scalar \(\delta\)-shell interactions

Cites Work

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• Shell interactions for Dirac operators
• Hardy spaces, singular integrals and the geometry of Euclidean domains of locally finite perimeter
• Radial symmetry for elliptic boundary-value problems on exterior domains
• Radial symmetry for an electrostatic, a capillarity and some fully nonlinear overdetermined problems on exterior domains
• Dirac operators with a spherically symmetric δ-shell interaction
• Variational methods in relativistic quantum mechanics
• Self-adjoint extensions of restrictions
• Shell Interactions for Dirac Operators: On the Point Spectrum and the Confinement
• Krein's resolvent formula for self-adjoint extensions of symmetric second-order elliptic differential operators
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)

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