PT-symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras
PT-symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras
Günther, U.; Kuzhel, S.
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.
Keywords: PT quantum mechanics; non-Hermitian Hamiltonians; gauge theory; Abelian gauge field; non-Abelian gauge field; Cartan decomposition; compact and noncompact components; Lie triple system; Clifford algebra; ultra-localized potential; Krein space; J-selfadjoint extension; Jaynes-Cummings system; multilevel artificial atoms; cavity QED; transmon states
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Journal of Physics A 43(2010), 392002
DOI: 10.1088/1751-8113/43/39/392002
ISSN: 1751-8121
Cited 18 times in Scopus
Permalink: https://www.hzdr.de/publications/Publ-14933