Scattering theory for the Dirac operator with a long-range electromagnetic potential

DOI10.1006/jfan.2001.3742zbMath0996.35056OpenAlexW2010643892MaRDI QIDQ5944723

Dimitri Yafaev, Yannick Gâtel

Publication date: 4 November 2002

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2001.3742

zbMATH Keywords

Dirac equationlimiting absorption principleasymptotics for large timeseikonal and transport equationslong-range scattering theory for the Dirac operator

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Boundary value problems for PDEs with pseudodifferential operators (35S15) PDEs in connection with quantum mechanics (35Q40) (2)-body potential quantum scattering theory (81U05)

Related Items (8)

High‐energy and smoothness asymptotic expansion of the scattering amplitude for the Dirac equation and application ⋮ Holomorphic family of Dirac-Coulomb Hamiltonians in arbitrary dimension ⋮ Inverse scattering at fixed energy in de Sitter-Reissner-Nordström black holes ⋮ Spectral theory of Dirac operators with potentials diverging at infinity ⋮ Scattering theory for massless Dirac fields with long-range potentials ⋮ Propagation estimates for Dirac operators and application to scattering theory. ⋮ Time-dependent scattering theory for charged Dirac fields on a Reissner–Nordström black hole ⋮ Infrared problem in perturbative quantum field theory

Cites Work

• The nonrelativistic limit of modified wave operators for Dirac operators
• Scattering theory by Enss' method for operator valued matrices: Dirac operator in an electric field
• Remarks on the spectral theory for the multiparticle-type Schrödinger operator
• Absolutely continuous spectrum of Dirac operators for long-range potentials
• On the point spectrum of Dirac operators
• Short-range scattering in long-range magnetic fields: The relativistic case
• Spectral analysis of N-body Schrödinger operators
• Absence of singular continuous spectrum for certain self-adjoint operators
• The scattering amplitude for the Schrödinger equation with a long-range potential
• Scattering theory: some old and new problems
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