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.

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

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• 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
• Three-Hilbert-Space Formulation of Quantum Mechanics
• Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems
• A Positive-Definite Scalar Product for Free Proca Particle
• Adiabatic time-dependent metrics in PT-symmetric quantum theories

Cited by in corpus (5)

• Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics
• Composite quantum Coriolis forces
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation
• Three alternative model-building strategies using quasi-Hermitian time-dependent observables
• Quantum mechanics using two auxiliary inner products