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

Communications in Theoretical Physics

Generalized Weyl Ordering and Nonlinear Coherent States

Fan Hong-Yi

Published Dec 15, 2002• 3 citations
Publisher

Abstract

In the context of the nonlinear coherent state (NLCS) theory we introduce the generalized Weyl ordering operator formulation. The corresponding generalized Wigner operator turns out to be the Weyl ordered Dirac δ-operator functions. The completeness relation of NLCS is recast into generalized Weyl ordering form. The relationship between normal ordering, antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistent theory for NLCS.

DOI
10.1088/0253-6102/38/6/729

Related papers

Generalized Weyl Ordering and Nonlinear Coherent States

FANHong-Yi, Hong-Yi

In the context of the nonlinear coherent state (NLCS) theory we introduce the generalized Weyl orderingoperator formulation. The corresponding generalized Wigner operator turns out to be the Weyl ordered Dirac δ-operatorfunctions. The completeness relation of NLCS is recast into generalized Weyl ordering form. The relationship betweennormal ordering, antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistenttheory for NLCS.

理论物理通讯:英文版•Jan 1, 2002•0 citations

New Approach for Introducing Wigner Function,Weyl Correspondence and the Coherent State Representation of Wigner Operator

Fan Hong‐Yi

By using the normal ordering form of the coordinate,momentum completeness,we directly and concisely introduce the Wigner operator and then illustrate its relation with the Weyl correspondence.The coherent state representation of the Wigner operator is also neatly derived.

Acta Sinica Quantum Optica•Jan 1, 2010•0 citations

WEYL ORDERING FOR ENTANGLED STATE REPRESENTATION

Hong-Yi Fan, Yue Fan

We derive a new Weyl ordering operator formula which recasts given operators into Weyl ordering. In so doing, the Weyl ordering formulation of the entangled state representation is obtained, which turns out to be the Weyl ordered Dirac δ-operator functions. The Weyl ordering of the Wigner operator and squeezing operator in entangled state representation are also deduced.

International Journal of Modern Physics A•Feb 20, 2002•43 citations

Coherent State Formulation of the Weyl Correspondence and the Wigner Function

Fan Hong-Yi, Ruan Tu-Nan

We point out that there is a close connection between the Weyl correspondence and coherent state correspondence. By virtue of differential and integral method within normal ordered products we demonstrate that the essence of the Weyl correspondence is just coherent state correspondence in both boson and fermion cases. Furthermore, coherent state form and explicit operator form for the Wigner function are given. With these forms we can derive some important operator formulas from the Weyl correspondence. The Wigner function's zero-point value is also discussed.

Communications in Theoretical Physics•Nov 1, 1983•48 citations

-representation, positive -representation, and antinormally ordering expansion of density matrices in nonlinear coherent states

Hong-Yi Fan, Yue Fan, Junhua Chen

Based on the newly constructed overcompleteness relation of the nonlinear coherent states (NLCSs) and corresponding 𝒫-representation we derive: (1) a new antinormally ordered expansion of density matrices; and (2) the corresponding positive 𝒫-representation. Our derivation employs the technique of integration within an ordered product of nonlinear Bose operator functions. A relationship between the positive 𝒫-representation and the generalized characteristic function in the context of NLCSs is also obtained.

Journal of Optics B Quantum and Semiclassical Optics•Sep 2, 2002•2 citations

New Formulation of Weyl Quantization Scheme in Coherent State Representation

Tang-Kun Liu, Hong-Yi Fan

By virtue of the technique of integration within an ordered product of operators we present a new formulation of the Weyl quantization scheme in the coherent state representation, which not only brings convenience for calculating the Weyl correspondence of normally ordered operators, but also directly leads us to find both the coherent state representation and the Weyl ordering representation of the Wigner operator.

Communications in Theoretical Physics•Jan 1, 2011•1 citation
In the context of the nonlinear coherent state (NLCS) theory we introduce the generalized Weyl ordering operator formulation. The corresponding generalized Wigner operator turns out to be the Weyl ordered Dirac δ-operator functions. The completeness relation of NLCS is recast into generalized Weyl ordering form. The relationship between normal ordering, antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistent theory for NLCS.
We point out that there is a close connection between the Weyl correspondence and coherent state correspondence. By virtue of differential and integral method within normal ordered products we demonstrate that the essence of the Weyl correspondence is just coherent state correspondence in both boson and fermion cases. Furthermore, coherent state form and explicit operator form for the Wigner function are given. With these forms we can derive some important operator formulas from the Weyl correspondence. The Wigner function's zero-point value is also discussed.
Based on the newly constructed overcompleteness relation of the nonlinear coherent states (NLCSs) and corresponding 𝒫-representation we derive: (1) a new antinormally ordered expansion of density matrices; and (2) the corresponding positive 𝒫-representation. Our derivation employs the technique of integration within an ordered product of nonlinear Bose operator functions. A relationship between the positive 𝒫-representation and the generalized characteristic function in the context of NLCSs is also obtained.