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

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.