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Generalized Wigner Functions for Damped Systems in deformation quantization

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Communications in Theoretical Physics 2007年第2X期48卷 255-260页

作者： HENG Tai-Hua JING Si-Cong Department of Modern Physics University of Science and Technology of China Hefei 230026 China

quantization of damped systems usually gives rise to complex spectra and corresponding resonant states, which do not belong to the Hilbert space. Therefore, the standard form of calculating Wigner function （WF） does not work for these systems. In this paper we show that in order to let WF satisfy a ,-genvalue equation for the damped systems, one must modify its standard form slightly, and this modification exactly coincides with the results derived from a ＊-Exponential expansion in deformation quantization.

关键词： Wigner function damped system deformation quantization

The Enhanced Period Map and Equivariant deformation quantizations of Nilpotent Orbits

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Acta Mathematica Sinica,English Series 2024年第3期40卷 885-934页

作者： Shi Lin YU Department of Mathematics School of Mathematical SciencesXiamen UniversityXiamen 361005P.R.China

In a previous paper,the author and his collaborator studied the problem of lifting Hamil-tonian group actions on symplectic varieties and Lagrangian subvarieties to their graded deformation quantizations and apply the general results to coadjoint orbit method for semisimple Lie *** even quantizations were considered *** this paper,these results are generalized to the case of general quantizations with arbitrary *** key step is to introduce an enhanced version of the(truncated)period map defined by Bezrukavnikov and Kaledin for quantizations of any smooth sym-plectic variety X,with values in the space of Picard Lie algebroid over *** an application,we study quantizations of nilpotent orbits of real semisimple groups satisfying certain codimension condition.

关键词： Coadjoint orbit method deformation quantization Harish-Chandra modules semisimple Liegroups

Realization of Poisson enveloping algebra

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Frontiers of Mathematics in China 2018年第4期13卷 999-1011页

作者： Can ZHU Yaxiu WANG College of Science University of Shanghai for Science and Technology Shanghai 200093 China

For a Poisson algebra, the category of Poisson modules is equivalent to the module category of its Poisson enveloping algebra, where the Poisson enveloping algebra is an associative one. In this article, for a Poisson structure on a polynomial algebra S, we first construct a Poisson algebra R, then prove that the Poisson enveloping algebra of S is isomorphic to the specialization of the quantized universal enveloping algebra of R, and therefore, is a deformation quantization of R.

关键词： Poisson enveloping algebra quantized universal enveloping algebra deformation quantization

Cohomology structure for a Poisson algebra:Ⅱ

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Science China Mathematics 2021年第5期64卷 903-920页

作者： Yan-Hong Bao Yu Ye School of Mathematical Sciences Anhui UniversityHefei 230601China School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026China Wu Wen-Tsun Key Laboratory of Mathematics USTCChinese Academy of SciencesHefei 230026China

For a Poisson algebra,we prove that the Poisson cohomology theory introduced by Flato et al.(1995)is given by a certain derived *** show that the(generalized)deformation quantization is equivalent to the formal deformation for Poisson algebras under certain mild *** we construct a long exact sequence,and use it to calculate the Poisson cohomology groups via the Yoneda-extension groups of certain quasi-Poisson modules and the Lie algebra cohomology groups.

关键词： Poisson algebra Poisson cohomology formal deformation deformation quantization

A New Type of Seiberg-Witten Map and Its Application

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Communications in Theoretical Physics 2008年第11期50卷 1077-1080页

作者： GUAN Yong LIN Bing-Sheng JING Si-Cong Department of Modern Physics University of Science and Technology of China Hefei 230026 China

deformation quantization is a powerful tool to deal with systems in noncommutative space to get their energy spectra and corresponding Wigner functions, especially for the ease of both coordinates and momenta being noneommutative. In order to simplify solutions of the relevant .-genvalue equation, we introduce a new kind of Seiberg Witten-like map to change the variables of the noncommutative phase space into ones of a commutative phase space, and demonstrate its role via an example of two-dimensional oscillator with both kinetic and elastic couplings in the noneommutative phase space.

关键词： deformation quantization noncommutative phase space coupled oscillator

A Note on Wigner Functions and *-Genvalue Equation

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Communications in Theoretical Physics 2009年第4期51卷 605-608页

作者： JING Si-Cong LIN Bing-Sheng Department of Modern Physics,University of Science and Technology of China,Hefei 230026,China Department of Modern Physics University of Science and Technology of China Hefei 230026 China

In deformation quantization,static Wigner functions obey functional *-genvalue equation,which is equiv-alent to time-independent Schr■dinger equation in Hilbert space operator formalism of quantum *** equiv-alence is proved mostly for Hamiltonian with form H=（1/2）■;+V（■）[***,***.60（1964）581].In this note we generalize this proof to a very general Hamiltonian H（■,■）and give examples to support it.

关键词： Wigner function *-genvalue equation deformation quantization