Non-Hermitian Heisenberg representation

Abstract

In a way paralleling the recently accepted non-Hermitian version of quantum mechanics in its Schrödinger representation (working often with the innovative and heuristically productive concept of $\mathcal{P}\mathcal{T}-$symmetry), it is demonstrated that it is also possible to construct an analogous non-Hermitian version of quantum mechanics in its Heisenberg representation.

arXiv comment10 pp., prepared for the PHHQP XV conference in Palermo: http://www.math.unipa.it/~phhqp15/

References in corpus (15)

• Making Sense of Non-Hermitian Hamiltonians
• Pseudo-Hermitian Representation of Quantum Mechanics
• Time-dependent version of cryptohermitian quantum theory
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Time evolution of non-Hermitian Hamiltonian systems
• Non-Hermitian quantum dynamics of a two-level system and models of dissipative environments
• Time Dependent $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Three-Hilbert-Space Formulation of Quantum Mechanics
• Quantum Mechanics of Klein-Gordon-Type Fields and Quantum Cosmology
• Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems
• Geometric Phase in PT-Symmetric Quantum Mechanics
• Classical limit of non-Hermitian quantum dynamics - a generalised canonical structure
• A Positive-Definite Scalar Product for Free Proca Particle
• Adiabatic time-dependent metrics in PT-symmetric quantum theories
• Crypto-unitary forms of quantum evolution operators

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• Non-Hermitian coupled cluster method for non-stationary systems and its interaction-picture reinterpretation
• Repeatability of measurements: Equivalence of hermitian and non-hermitian observables
• Wheeler-DeWitt equation and the applicability of crypto-Hermitian interaction representation in quantum cosmology
• Hybrid form of quantum theory with non-Hermitian Hamiltonians
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Composite quantum Coriolis forces
• Broken Hermiticity phase transition in Bose-Hubbard model
• Hermitian--to--quasi-Hermitian quantum phase transitions
• Heisenberg and Heisenberg-Like Representations via Hilbert Space Bundle Geometry in the Non-Hermitian Regime
• Quantization of Big Bang in crypto-Hermitian Heisenberg picture
• Non-stationary non-Hermitian "wrong-sign'' quantum oscillators and their meaningful physical interpretation
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation
• Three alternative model-building strategies using quasi-Hermitian time-dependent observables
• Consistent treatment of quantum systems with a time-dependent Hilbert space
• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics
• Mutual compatibility/incompatibility of quasi-Hermitian quantum observables
• Quantum mechanics using two auxiliary inner products