Linear phase space deformations with angular momentum symmetry

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2018-03-23 DOI:10.3934/jgm.2019003
Claudio Meneses
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Abstract

Motivated by the work of Leznov--Mostovoy, we classify the linear deformations of standard $2n$-dimensional phase space that preserve the obvious symplectic $\mathfrak{o}(n)$-symmetry. As a consequence, we describe standard phase space, as well as $T^{*}S^{n}$ and $T^{*}\mathbb{H}^{n}$ with their standard symplectic forms, as degenerations of a 3-dimensional family of coadjoint orbits, which in a generic regime are identified with the Grassmannian of oriented 2-planes in $\mathbb{R}^{n+2}$.
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具有角动量对称的线性相空间变形
在Leznov—Mostovoy工作的激励下,我们对保持明显的辛$\mathfrak{o}(n)$对称性的标准$2n$维相空间的线性变形进行了分类。因此,我们将标准相空间,以及$T^{*}S^{n}$和$T^{*}\mathbb{H}} {n}$及其标准辛形式描述为三维共轨族的退化,在一般情况下,这些共轨族在$\mathbb{R}^{n+2}$中被识别为有向2平面的Grassmannian。
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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