General theory of regular biorthogonal pairs and its physical operators

DOI10.1063/1.4961323zbMath1344.81177arXiv1604.01967OpenAlexW3099997814MaRDI QIDQ2820932

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Publication date: 12 September 2016

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

Full work available at URL: https://arxiv.org/abs/1604.01967

Mathematics Subject Classification ID

Many-body theory; quantum Hall effect (81V70) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (13)

Generalized Riesz systems and orthonormal sequences in Krein spaces ⋮ Some perturbation results for quasi-bases and other sequences of vectors ⋮ Unbounded Hamiltonians generated by Parseval frames ⋮ Order structures of \((\mathcal{D,E})\)-quasi-bases and constructing operators for generalized Riesz systems ⋮ Gibbs states, algebraic dynamics and generalized Riesz systems ⋮ Dynamics of finite dimensional non-hermitian systems with indefinite metric ⋮ Non-self-adjoint Hamiltonians defined by sesquilinear forms and their physical applications ⋮ Biorthogonal vectors, sesquilinear forms, and some physical operators ⋮ Towards generalized Riesz systems theory ⋮ Regular biorthogonal pairs and pseudo-bosonic operators ⋮ Generalized Riesz systems and quasi bases in Hilbert space ⋮ Semi-regular biorthogonal pairs and generalized Riesz bases ⋮ An algebraic approach of non-self-adjoint Hamiltonians in Krein spaces

Cites Work

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• Non-self-adjoint Hamiltonians defined by generalized Riesz bases
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• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• (Regular) pseudo-bosons versus bosons
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• Pseudobosons, Riesz bases, and coherent states
• More mathematics for pseudo-bosons
• Non-self-adjoint hamiltonians defined by Riesz bases

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