P,T,PT, and CPT invariance of Hermitian Hamiltonians

Abstract

Currently, it has been claimed that certain Hermitian Hamiltonians have parity (P) and they are PT-invariant. We propose generalized definitions of time-reversal operator (T) and orthonormality such that all Hermitian Hamiltonians are P, T, PT, and CPT invariant. The PT-norm and CPT-norm are indefinite and definite respectively. The energy-eigenstates are either E-type (e.g., even) or O-type (e.g., odd). C mimics the charge-conjugation symmetry which is recently found to exist for a non-Hermitian Hamiltonian. For a Hermitian Hamiltonian it coincides with P.

arXiv comment8 pages, no figures, text modified, to appear in Phys. Lett. A

References in corpus (16)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• PT -symmetric harmonic oscillators
• Complex periodic potentials with real band spectra
• sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
• A PT-Invariant Potential With Complex QES Eigenvalues
• Generalized Continuity Equation and Modified Normalization in PT-Symmetric Quantum Mechanics
• A new PT symmetric complex Hamiltonian with a real spectra
• Exact solution for Morse oscillator in PT-symmetric quantum mechanics
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the co-ordinate : real spectrum of complex potentials
• Space of State Vectors in PT Symmetrical Quantum Mechanics
• The energy spectrum of complex periodic potentials of the Kronig-Penney type
• All Hermitian Hamiltonians Have Parity

Cited by in corpus (18)

• Making Sense of Non-Hermitian Hamiltonians
• Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics
• Spectra of PT-Symmetric Operators and Perturbation Theory
• Finite-Dimensional PT-Symmetric Hamiltonians
• PT/Non-PT Symmetric and Non-Hermitian Poschl-Teller-Like Solvable Potentials via Nikiforov-Uvarov Method
• Quantum Mechanics of Proca Fields
• $PT$ symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum
• C, PT, and CPT invariance of pseudo-Hermitian Hamiltonians
• Supersymmetric solution of PT-/non-PT-symmetric and non-Hermitian Morse potential is studied to get real and Supersymmetric Solution of PT-/Non-PT-Symmetric and Non-Hermitian Morse Potential via Hamiltonian Hierarchy Method
• Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry
• Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
• Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries
• Pseudo-reality and pseudo-adjointness of Hamiltonians
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra
• A Novel SUSY Energy Bound States Treatment of the Klein-Gordon Equation with PT-Supersymmetric and q-Deformed Hulthen Potential
• Canonical Expansion of PT-Symmetric Operators and Perturbation Theory
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor