Sign of a perturbed massive Dirac operator and associated Fredholm module

DOI10.1016/j.geomphys.2018.09.017zbMath1414.35191OpenAlexW2903538438WikidataQ128843389 ScholiaQ128843389MaRDI QIDQ669597

Galina Levitina, Dmitriy Zanin, Pheodor A. Sukochev

Publication date: 15 March 2019

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2018.09.017

zbMATH Keywords

Fredholm modulemassive Dirac operatorquantised derivativeweak Schatten ideals

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Integral operators (45P05) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (3)

Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori ⋮ Noncommutative geometry for symmetric non-self-adjoint operators ⋮ Quantum differentiability on noncommutative Euclidean spaces

Cites Work

• Multiple operator integrals in perturbation theory
• Singular traces. Theory and applications
• Absolutely continuous spectrum of a Dirac operator in the case of a positive mass
• The index formula and the spectral shift function for relatively trace class perturbations
• Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators
• Nearly weakly orthonormal sequences, singular value estimates, and Calderon-Zygmund operators
• Noncommutative geometry, quantum fields and motives
• Functional analysis, Sobolev spaces and partial differential equations
• The action functional in non-commutative geometry
• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes
• Double operator integrals in a Hilbert space
• Schatten class estimates for the Riesz map of massless Dirac operators
• Perturbation theory for linear operators.
• Schatten classes and commutators of singular integral operators
• The local index formula in noncommutative geometry
• Integration in quasi-Banach spaces and the fundamental theorem of calculus
• Limiting absorption principle at critical values for the Dirac operator
• Quantum differentiability of essentially bounded functions on Euclidean space
• On the spectrum of magnetic Dirac operators with Coulomb-type perturbations
• An introduction to noncommutative geometry
• Unbounded Fredholm modules and double operator integrals
• HANKEL OPERATORS OF CLASS $ \mathfrak{S}_p$ AND THEIR APPLICATIONS (RATIONAL APPROXIMATION, GAUSSIAN PROCESSES, THE PROBLEM OF MAJORIZING OPERATORS)
• Unbounded Fredholm Modules and Spectral Flow
• On integrability in F-spaces
• Absence of eigenvalues of Dirac operators with potentials diverging at in-finity
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