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.

11 pages

References in corpus (17)

• Charge insensitive qubit design derived from the Cooper pair box
• Making Sense of Non-Hermitian Hamiltonians
• Visualization of Branch Points in PT-Symmetric Waveguides
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• n-ary algebras: a review with applications
• The Naimark dilated PT-symmetric brachistochrone
• PT-Symmetric Wave Chaos
• On the Lie-algebraic origin of metric 3-algebras
• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• Ternary Virasoro - Witt Algebra
• The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes
• Nonunique C operator in PT Quantum Mechanics
• General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space
• Thermal Excitation of Multi-Photon Dressed States in Circuit Quantum Electrodynamics
• Bi-element representations of ternary groups
• Gauging non-Hermitian Hamiltonians
• Symmetric bundles and representations of Lie triple systems

Cited by in corpus (6)

• Erlangen Programme at Large: An Overview
• On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators
• Erlangen Programme at Large 3.1: Hypercomplex Representations of the Heisenberg Group and Mechanics
• On elements of the Lax-Phillips scattering scheme for PT-symmetric operators
• Weight modules over split Lie algebras
• Artificial Hawking radiation, weak pseudo-Hermiticity and Weyl semimetal blackhole analogy