The topology and geometry of self-adjoint and elliptic boundary conditions for Dirac and Laplace operators

DOI10.1142/S0219887815610071zbMath1331.58021arXiv1510.08136WikidataQ62560978 ScholiaQ62560978MaRDI QIDQ3455873

Alberto Ibort, Giuseppe Marmo, Manuel Asorey

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/1510.08136

zbMATH Keywords

Dirac operatorLaplace operatorelliptic operatorCayley transformself-adjoint extension

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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Dai-Freed theorem and topological phases of matter ⋮ Quantum magnetic billiards: boundary conditions and gauge transformations ⋮ Boundaries without boundaries ⋮ One-dimensional scattering of fermions in double Dirac delta potentials ⋮ Hyperspherical \(\delta\)-\(\delta'\) potentials ⋮ Moving walls and geometric phases ⋮ Dirac-like operators on the Hilbert space of differential forms on manifolds with boundaries ⋮ Admissible boundary conditions for Hamiltonian field theories ⋮ Quantum cavities with alternating boundary conditions ⋮ The critical transition of Coulomb impurities in gapped graphene ⋮ Self-adjoint extensions and unitary operators on the boundary ⋮ Finite element method to solve the spectral problem for arbitrary self-adjoint extensions of the Laplace-Beltrami operator on manifolds with a boundary ⋮ Free fermions and the classical compact groups ⋮ Field fluctuations and Casimir energy of 1D-fermions ⋮ Boundary conditions for the quantum Hall effect

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