\mathcal P\mathcal T-symmetry, Cartan decompositions, Lie triple systems and Krein space-related Clifford algebras

2010/06/06 by Uwe Guenther, Uwe Günther, Sergii Kuzhel · 17 citations
Mathematics · Physics and Astronomy · #Abelian group #Algebra over a field #Clifford algebra #Gauge theory #Geometry #Interpretation (philosophy) #Lie algebra #Lie group #Mathematical physics #Mathematics #Parity (physics) #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Space (punctuation) #Symmetry (geometry) #Topological Materials and Phenomena #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/1751-8113/43/39/392002

published in Journal of Physics A Mathematical and Theoretical 43(39), 392002 (Institute of Physics) · 11 pages

arxiv created 2010/06/06 · openalex publication_date 2010/09/01 · arxiv updated 2014/11/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Gauged PT quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan decompositions. A Lie triple structure is found and an interpretation as PT-symmetrically generalized Jaynes-Cummings model is possible with close relation to recently studied cavity QED setups with transmon states in multilevel artificial atoms. For models with Abelian gauge potentials a hidden Clifford algebra structure is found and used to obtain the fundamental symmetry of Krein space related J-selfadjoint extensions for PTQM setups with ultra-localized potentials.

Citations

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