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arXiv · 1006.1134

PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras

Uwe Guenther·Sergii Kuzhel
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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.

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Uwe Guenther, Sergii Kuzhel. 2010-06-06. PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras. https://doi.org/10.1088/1751-8113%2F43%2F39%2F392002

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