On the theory of self-adjoint extensions of symmetric operators and its applications to quantum physics

DOI10.1142/S0219887815600051zbMath1327.81199arXiv1502.05229OpenAlexW2964066020MaRDI QIDQ3455871

Juan Manuel Pérez-Pardo, Alberto Ibort

Publication date: 11 December 2015

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.05229

zbMATH Keywords

Dirac operatorquadratic formsLaplace-Beltrami operatorself-adjoint extensionsbipartite system with boundaryextensions of not semibounded operators

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Integration on manifolds; measures on manifolds (58C35) Applications of global differential geometry to the sciences (53C80) Invariance and symmetry properties for PDEs on manifolds (58J70) Differential forms in global analysis (58A10) Applications of functional analysis in quantum physics (46N50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Boundary value problems on manifolds (58J32) Spectral theory; eigenvalue problems on manifolds (58C40) Time-dependent Schrödinger equations and Dirac equations (35Q41) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Quantum control (81Q93)

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Cites Work

• Perturbation theory for linear operators.
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