Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries

Abstract

We study certain linear and antilinear symmetry generators and involution operators associated with pseudo-Hermitian Hamiltonians and show that the theory of pseudo-Hermitian operators provides a simple explanation for the recent results of Bender, Brody and Jones (quant-ph/0208076) on the CPT-symmetry of a class of PT-symmetric non-Hermitian Hamiltonians. We present a natural extension of these results to the class of diagonalizable pseudo-Hermitian Hamiltonians H with a discrete spectrum. In particular, we introduce generalized parity ($\mathcal{P}$), time-reversal ($\mathcal{T}$), and charge-conjugation ($\mathcal{C}$) operators and establish the $\mathcal{P}\mathcal{T}$- and $\mathcal{C}\mathcal{P}\mathcal{T}$-invariance of H.

25 pages, slightly revised version, accepted for publication in J. Math. Phys

References in corpus (3)

• Complex Extension of Quantum Mechanics
• Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations
• Pseudo-Hermiticity for a Class of Nondiagonalizable Hamiltonians

Cited by in corpus (139)

• Making Sense of Non-Hermitian Hamiltonians
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Pseudo-Hermitian Representation of Quantum Mechanics
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Exact PT-Symmetry Is Equivalent to Hermiticity
• New topological invariants in non-Hermitian systems
• PT-Symmetric Electronics
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• The ODE/IM Correspondence
• Non-Hermitian Hamiltonians and no-go theorems in quantum information
• PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations
• Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
• Metric Operator in Pseudo-Hermitian Quantum Mechanics and the Imaginary Cubic Potential
• Quantum Mechanics of Klein-Gordon-Type Fields and Quantum Cosmology
• Delta-Function Potential with a Complex Coupling
• Quasi-Hermiticity in infinite-dimensional Hilbert spaces
• Biorthogonal Quantum Systems
• Topological phases in Kitaev chain with imbalanced pairing
• Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics
• Parity-time symmetry in optical microcavity systems
• Completeness and Orthonormality in PT-symmetric Quantum Systems
• d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass
• Fermionic coherent states for pseudo-Hermitian two-level systems
• On the invariant method for the time-dependent non-Hermitian Hamiltonians
• Quantum Mechanics of Klein-Gordon Fields I: Hilbert Space, Localized States, and Chiral Symmetry
• Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism
• Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
• Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report
• On the pseudo-Hermitian nondiagonalizable Hamiltonians
• Finite-Dimensional PT-Symmetric Hamiltonians
• Pseudo-Hermitian Quantum Mechanics with Unbounded Metric Operators
• Non-Hermitian Dynamic Strings and Anomalous Topological Degeneracy on non-Hermitian Toric-code Model with Parity-time Symmetry
• Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay
• On integrable wave interactions and Lax pairs on symmetric spaces
• A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields
• Application of Pseudo-Hermitian Quantum Mechanics to a PT-Symmetric Hamiltonian with a Continuum of Scattering States
• On the N-wave Equations with PT-symmetry
• The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes
• $\mathcal{P}\mathcal{T}$-symmetric, non-Hermitian quantum many-body physics -- a methodological perspective
• (1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric
• PT Symmetry as a Generalization of Hermiticity
• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
• Solvability and PT-symmetry in a double-well model with point interactions
• Non-Hermitian quantum systems and their geometric phases
• $\eta$-weak-Pseudo-Hermiticity generators and exact solvability
• Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics
• A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models
• Quantum Mechanics of Proca Fields
• Generalized Swanson models and their solutions
• Real Description of Classical Hamiltonian Dynamics Generated by a Complex Potential
• Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem
• Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
• From Generalized Dirac Equations to a Candidate for Dark Energy
• Exactly solvable time-dependent pseudo-Hermitian $su$(1,1) Hamiltonian models
• Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions
• C, PT, and CPT invariance of pseudo-Hermitian Hamiltonians
• Quantum Mechanics of a Photon
• Massive gauge particles versus Goldstone bosons in non-Hermitian non-Abelian gauge theory
• The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation
• Non-Hermitian von Roos Hamiltonian's $\eta$-weak-pseudo-Hermiticity, isospectrality and exact solvability
• Non-Hermitian Hamiltonians with a Real Spectrum and Their Physical Applications
• Pseudo-Hermitian Quantum Dynamics of Tachyonic Spin-1/2 Particles
• Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
• An alternative construction of the positive inner product in non-Hermitian quantum mechanics
• Emergent parallel transport and curvature in Hermitian and non-Hermitian quantum mechanics
• First-order intertwining operators with position dependent mass and $\eta$- weak-psuedo-Hermiticity generators
• Nonlinear Non-Hermitian Landau-Zener-Stückelberg-Majorana interferometry
• Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
• Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach
• Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries
• An alternative construction of the positive inner product for pseudo-Hermitian Hamiltonians: Examples
• Classical oscillator with position-dependent mass in a complex domain
• Nonlocal reductions of the Ablowitz-Ladik equation
• Analytically solvable $2\times 2$ $PT$-symmetry dynamics from su(1,1)-symmetry problems
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Myers-Pospelov Model as an Ensemble of Pais-Uhlenbeck Oscillators: Unitarity and Lorentz Invariance Violation
• Hermitian Hamiltonian equivalent to a given non-Hermitian one. Manifestation of spectral singularity
• Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?
• Point Interactions, Metamaterials, and PT-Symmetry
• Investigation of PT-symmetric Hamiltonian systems from an alternative point of view
• Unbounded C-symmetries and their nonuniqueness
• Resonant generation of $p$-wave Cooper pair in non-Hermitian Kitaev chain at exceptional point
• Coherent states of non-Hermitian quantum systems
• Observables in non-Hermitian systems: A methodological comparison
• p-Adic Schrödinger-Type Operator with Point Interactions
• PT-symmetric regularizations in supersymmetric quantum mechanics
• Quantum Graphs: $\mathcal{P}\mathcal{T}$-symmetry and reflection symmetry of the spectrum
• Pseudo-reality and pseudo-adjointness of Hamiltonians
• Hybrid form of quantum theory with non-Hermitian Hamiltonians
• On nonlocal reductions of the multi-component nonlinear Schrodinger equation on symmetric spaces
• Spontaneous breaking of permutation symmetry in pseudo-Hermitian quantum mechanics
• Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement
• A possible method for non-Hermitian and non-$PT$-symmetric Hamiltonian systems
• Exact Solutions of the Schrödinger Equation with position-dependent effective mass via general point canonical transformation
• $\mathcal{P}\mathcal{T}$ symmetric models with nonlinear pseudo supersymmetry
• Quantum mold casting for topological insulating and edge states
• A Novel SUSY Energy Bound States Treatment of the Klein-Gordon Equation with PT-Supersymmetric and q-Deformed Hulthen Potential
• Exact quantization conditions and full transseries structures for $\mathcal{P}\mathcal{T}$ symmetric anharmonic oscillators
• Operator description for thermal quantum field theories on an arbitrary path in the real time formalism
• Neutrino Helicity Reversal and Fundamental Symmetries
• Tachyonic Field Theory and Neutrino Mass Running
• On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm
• Lower bound of minimal time evolution in quantum mechanics
• Non-Hermitian Hamiltonian versus E=0 localized states
• Non-Hermitian Generalization of Rayleigh-Schrödinger Perturbation Theory
• Topological phase in Kitaev chain with spatially separated pairing processes
• Reality and hermiticity from maximizing overlap in the future-included complex action theory
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• A controllable anti-P-pseudo-Hermitian mechanical system and its application
• Pseudo-Hermiticity, PT-symmetry, and the Metric Operator
• Heisenberg and Heisenberg-Like Representations via Hilbert Space Bundle Geometry in the Non-Hermitian Regime
• Non-Hermitian quantum walks and non-Markovianity: the coin-position interaction
• Dirac Hamiltonian with Imaginary Mass and Induced Helicity-Dependence by Indefinite Metric
• Spherical-separablility of non-Hermitian Hamiltonians and pseudo-PT-symmetry
• Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space
• Spherical-separablility of non-Hermitian Dirac Hamiltonians and pseudo-PT-symmetry
• Probability Interpretation for Klein-Gordon Fields and the Hilbert Space Problem in Quantum Cosmology
• Two dimensional non-Hermitian harmonic oscillator: coherent states
• Monopoles in non-Hermitian systems
• Reality from maximizing overlap in the periodic complex action theory
• Decomposition of a system in pseudo-Hermitian quantum mechanics
• Automatic hermiticity for mixed states
• Fixed lines in a non-Hermitian Kitaev chain with spatially balanced pairing processes
• $\mathcal{P}\mathcal{T}$-Symmetric Generalized Extended Momentum Operator
• Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: I. Inherited and genuine singularities
• Bosonic Holes in Quadratic Bosonic Systems
• Reality from maximizing overlap in the future-included real action theory
• Momentum relation and classical limit in the future-not-included complex action theory
• Anharmonic oscillators in the complex plane, $\mathcal{P}\mathcal{T}$-symmetry, and real eigenvalues
• On pseudo-Hermitian operators with generalized $\mathcal{C}$-symmetries
• Three-level Λ-type atomic systems with a Pseudo-Hermitian PT-symmetric Hamiltonian
• Neutrino Pair Cerenkov Radiation for Tachyonic Neutrinos
• $\mathcal{P}\mathcal{T}$-like phase transitions from square roots of supersymmetric Hamiltonians
• Emergence of Hermitian topology from non-Hermitian knots
• A new Berry phase term in parity-time symmetric non-Hermitian spin-1/2 quantum systems
• Reduced dynamics in quasi-Hermitian systems