Is Pseudo-Hermitian Quantum Mechanics an Indefinite-Metric Quantum Theory?

Abstract

With a view to eliminate an important misconception in some recent publications, we give a brief review of the notion of a pseudo-Hermitian operator, outline pseudo-Hermitian quantum mechanics, and discuss its basic difference with the indefinite-metric quantum mechanics. In particular, we show that the answer to the question posed in the title is a definite No.

7 pages, contributed to the meeting on Quantum Groups and Integrable Systems held in Prag, June 2003

References in corpus (3)

• Exact PT-Symmetry Is Equivalent to Hermiticity
• 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 (29)

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• Foldy-Wouthyusen Transformation and Semiclassical Limit for Relativistic Particles in Strong External Fields
• Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics
• Quantum Mechanics of Klein-Gordon Fields I: Hilbert Space, Localized States, and Chiral Symmetry
• Solvable PT-symmetric model with a tunable interspersion of non-merging levels
• Fragile PT-symmetry in a solvable model
• Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
• Hamilton Operator and the Semiclassical Limit for Scalar Particles in an Electromagnetic Field
• A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models
• Quantum Mechanics of Proca Fields
• Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation
• Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry
• Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
• Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?
• Linear representation of energy-dependent Hamiltonians
• On the K-theoretic classification of dynamically stable systems
• On the supersymmetry of the Klein-Gordon oscillator
• Lorentz Symmetric Quantum Field Theory for Symplectic Fermions
• Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
• Pseudo-Hermiticity, PT-symmetry, and the Metric Operator
• Locality, Correlations, Information, and non-Hermitian Quantum Systems
• Scattering in pseudo-Hermitian quantum field theory and causality violation
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space
• Quantum implementation of non-unitary operations with biorthogonal representations
• Pseudo-Hermitian systems, involutive symmetries and pseudofermions
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation
• Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics