\(\mathcal{PT}\)-symmetry in (generalized) effect algebras

DOI10.1007/S10773-010-0594-9zbMath1257.03094OpenAlexW2018893627MaRDI QIDQ539565

Jan Paseka

Publication date: 30 May 2011

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10773-010-0594-9

zbMATH Keywords

Hilbert spaceunbounded linear operatorsgeneralized effect algebra\(\mathcal{PT}\)-symmetrypartially ordered commutative grouppseudo-Hermitian quantum mechanics

Mathematics Subject Classification ID

Complemented lattices, orthocomplemented lattices and posets (06C15) Quantum logic (03G12) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (8)

Reply to the Comment on ‘The operational foundations of PT-symmetric and quasi-Hermitian quantum theory’ ⋮ On realization of partially ordered abelian groups ⋮ On realization of generalized effect algebras ⋮ Generalized effect algebras of bounded positive operators defined on Hilbert spaces ⋮ Considerable sets of linear operators in Hilbert spaces as operator generalized effect algebras ⋮ Weakly ordered partial commutative group of self-adjoint linear operators densely defined on Hilbert space ⋮ Representations of zero-cancellative pomonoids ⋮ Comment on ‘The operational foundations of PT-symmetric and quasi-Hermitian quantum theory’

Cites Work

• Effect algebras and unsharp quantum logics.
• Hilbert space operators in quantum physics
• Subalgebras, intervals, and central elements of generalized effect algebras
• Perturbation theory for linear operators.
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• ExactPT-symmetry is equivalent to Hermiticity
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
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