Noninvertible Bogoliubov transformations and instability of embedded eigenvalues

DOI10.1063/1.529248zbMath0741.47016OpenAlexW2095008858MaRDI QIDQ3980913

Asao Arai

Publication date: 26 June 1992

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

Full work available at URL: http://hdl.handle.net/2115/13675

zbMATH Keywords

selfadjoint operatorsScattering theoryembedded-eigenvaluesHamiltonians of models of a quantum harmonic oscillator coupled to a quantized scalar or radiation fieldnoninvertible Bogoliubov transformations in an abstract Boson Fock spacequadratic in the annihilation and the creation operators

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Linear symmetric and selfadjoint operators (unbounded) (47B25) Scattering theory of linear operators (47A40)

Related Items (3)

Scaling limit of a model of quantum electrodynamics ⋮ Observable effects and parametrized scaling limits of a model in nonrelativistic quantum electrodynamics ⋮ On the absence of eigenvectors of Hamiltonians in a class of massless quantum field models without infrared cutoff

Cites Work

• Perturbation of embedded eigenvalues: A general class of exactly soluble models in Fock spaces
• Spectral analysis of a quantum harmonic oscillator coupled to infinitely many scalar bosons
• Applications of a commutation formula
• An asymptotic analysis and its application to the nonrelativistic limit of the Pauli–Fierz and a spin-boson model
• On a model of a harmonic oscillator coupled to a quantized, massless, scalar field. I
• On a model of a harmonic oscillator coupled to a quantized massless, scalar field. II
• Rigorous theory of spectra and radiation for a model in quantum electrodynamics

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