# Quasi-Hermitian quantum mechanics in phase space

@article{Curtright2007QuasiHermitianQM, title={Quasi-Hermitian quantum mechanics in phase space}, author={Thomas L. Curtright and Andrzej Veitia}, journal={Journal of Mathematical Physics}, year={2007}, volume={48}, pages={102112-102112} }

We investigate quasi-Hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact results are easily obtained. We emphasize spatially periodic solutions, compute various distribution functions and phase-space metrics, and explore the relationships between them.

## 12 Citations

Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay

- PhysicsInternational Journal of Modern Physics B
- 2018

The Wigner–Weyl transform and phase space formulation of a density matrix approach are applied to a non-Hermitian model which is quadratic in positions and momenta. We show that in the presence of a…

On Wigner functions and a damped star product in dissipative phase-space quantum mechanics

- Physics
- 2008

Pseudo-Hermitian Representation of Quantum Mechanics

- Mathematics
- 2008

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a…

PT-symmetric quantum theory

- Physics
- 2015

The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to…

Biorthogonal quantum systems

- Physics
- 2007

Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporate all the structure of PT symmetric models, and allow for generalizations, especially…

COHERENT STATES AND SCHWINGER MODELS FOR PSEUDO GENERALIZATION OF THE HEISENBERG ALGEBRA

- Mathematics
- 2009

We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with $\mathcal{PT}$ and $\mathcal{C}$ symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs…

PT -Symmetric Interpretation of Double-Scaling

- Physics
- 2012

The conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the…

Tridiagonal {\cal PT} -symmetric N-by-N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime

- Physics
- 2007

A generic -symmetric Hamiltonian is assumed tridiagonalized and truncated to N < ∞ dimensions, H → H(chain model), and all its up–down symmetrized special cases with J = [N/2] real couplings are…

${\mathcal{P}}{\mathcal{T}}$-symmetric interpretation of the electromagnetic self-force

- Physics
- 2014

In 1980 Englert examined the classic problem of the electromagnetic self-force on an oscillating charged particle. His approach, which was based on an earlier idea of Bateman, was to introduce a…

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