Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

理论物理通讯:英文版

A Note on Wigner Functions and *-Genvalue Equation

Jing Jing, Si-Cong, Lin, Bing-Sheng

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

+V()[D。Fairlie, Proc。Camb。菲尔。Soc。60 (1964 ) 581 ] 。在这笔记,我们概括这个证明到很一般的 Hamiltonian (,) 并且给例子支持它。

Related papers

Wigner Functions for Non-Hamiltonian Systems on Noncommutative Space

衡太骅, 林冰生, 井思聪

我们在 noncommutative 空间为通用 non-Hamiltonian 系统建议 Wigner 功能的一种修改形式并且证明它满足相应 *-genvalue 方程。作为一个例子,另外,我们在 noncommutative 空格为一个 non-Hamiltonian 玩具模型导出准确精力系列和 Wigner 函数。[从作者抽象]

Chinese Physics Letters•Jan 1, 2008•0 citations

A Note on Wigner Functions and *-Genvalue Equation

Sicong Jing, Bing-Sheng Lin

In deformation quantization, static Wigner functions obey functional *-genvalue equation, which is equivalent to time-independent Schrodinger equation in Hilbert space operator formalism of quantum mechanics. This equivalence is proved mostly for Hamiltonian with form Ĥ = (1/2)2 + V() [D. Fairlie, Proc. Camb. Phil. Soc. 60 (1964) 581]. In this note we generalize this proof to a very general Hamiltonian Ĥ(, ) and give examples to support it.

Communications in Theoretical Physics•Apr 1, 2009•0 citations

Eigenfunctions and eigenvalues of the Wigner operator

A. D. Jannussis, N. Patargias

Physics Letters A•Jul 1, 1975•10 citations

Nonlocal, Non-Commutative Picture in Quantum Mechanics and Distinguished Continuous Canonical Maps

Tugrul Hakioglu

It is shown that continuous classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate ℏ-independent quantum nonlinear canonical maps. It is also shown that such maps act in the non-commutative phase space under the classical covariance. A crucial result of the work is that under the action of Poisson maps a local quantum mechanical picture is converted onto a non-local picture which is then represented in a non-local Hilbert space. On the other hand, it is known that a non-local picture is equivalent by the Weyl map to a non-commutative picture which, in the context of this work, corresponds to a phase space formulation of the theory. As a result of this equivalence, a phase space Schrödinger picture can be formulated. In particular, we obtain the ⋆-genvalue equation of Fairlie (1964 Proc. Camb. Phil. Soc. 60 581) and Curtright, Fairlie and Zachos (1998 Phys. Rev. D 58 025002). In a non-local picture entanglement becomes a crucial concept. The connection between the entanglement and non-locality is explored in the context of Poisson maps and specific examples of the generation of entanglement from a local wavefunction are provided by using the concept of generalized Bell states. The results obtained are also relevant for the non-commutative soliton picture in the non-commutative field theories. We elaborate on this in the context of the scalar non-commutative field theory.

arXiv:hep-th/0108125•Physica Scripta•Jan 1, 2002•1 citation

Dynamical Equations for the Wigner Functions

Jens Peder Dahl

Springer eBooks•Jan 1, 1983•20 citations

Wigner Function -A Formalism

Ijaz Durrani

•Jan 1, 2026•0 citations
It is shown that continuous classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate ℏ-independent quantum nonlinear canonical maps. It is also shown that such maps act in the non-commutative phase space under the classical covariance. A crucial result of the work is that under the action of Poisson maps a local quantum mechanical picture is converted onto a non-local picture which is then represented in a non-local Hilbert space. On the other hand, it is known that a non-local picture is equivalent by the Weyl map to a non-commutative picture which, in the context of this work, corresponds to a phase space formulation of the theory. As a result of this equivalence, a phase space Schrödinger picture can be formulated. In particular, we obtain the ⋆-genvalue equation of Fairlie (1964 Proc. Camb. Phil. Soc. 60 581) and Curtright, Fairlie and Zachos (1998 Phys. Rev. D 58 025002). In a non-local picture entanglement becomes a crucial concept. The connection between the entanglement and non-locality is explored in the context of Poisson maps and specific examples of the generation of entanglement from a local wavefunction are provided by using the concept of generalized Bell states. The results obtained are also relevant for the non-commutative soliton picture in the non-commutative field theories. We elaborate on this in the context of the scalar non-commutative field theory.