Extending \(\mathcal{P}\mathcal{T}\) symmetry from Heisenberg algebra to E2 Algebra

DOI10.1007/S10773-010-0511-2zbMath1216.81063arXiv1009.3236OpenAlexW3099392574MaRDI QIDQ539539

Carl M. Bender, R. J. Kalveks

Publication date: 30 May 2011

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

Full work available at URL: https://arxiv.org/abs/1009.3236

zbMATH Keywords

time reversalPT symmetryparitynon-HermitianE2 algebra

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quantum measurement theory, state operations, state preparations (81P15)

Related Items (6)

Critical parameters for non-Hermitian Hamiltonians ⋮ Spontaneous Breakdown of a PT-Symmetry in the Liouvillian Dynamics at a Non-Hermitian Degeneracy Point ⋮ Spontaneous PT-symmetry breaking for systems of noncommutative Euclidean Lie algebraic type ⋮ Stability boundaries of a Mathieu equation having \textit{PT} symmetry ⋮ Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra ⋮ On a model for rotational tunneling with a \(C_{6}\)-space-time symmetric analog

Cites Work

• Complex periodic potentials with real band spectra.
• Spectral equivalences, Bethe ansatz equations, and reality properties in 𝒫𝒯-symmetric quantum mechanics
• Supersymmetry and the spontaneous breakdown of 𝒫𝒯 symmetry
• Complex Extension of Quantum Mechanics
• 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
• 𝓟𝓣-symmetric quantum mechanics
• The ODE/IM correspondence

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