Singular Lagrangian varieties and related normal form problems in the semi-classical analysis of quantised integrable systems

量化可积系统半经典分析中的奇异拉格朗日簇及相关范式问题

• 批准号: 5419505
• 负责人: Dr. Mauricio Garay
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2004
• 资助国家: 德国
• 起止时间: 2003-12-31 至 2006-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5419505?language=en
• 关键词: Singular; Lagrangian; varieties; related; normal

The development of resurgent analysis has provided a new look on the perturbation series arising in quantum mechanics. These studies have in turn raised new attention on the theory of singular Lagrangian varieties in connection with the singular Bohr-Sommerfeld rules. For instance, problems such as the convergence of the series in the normal forms turned out to be of particular interest. The methods coming from algebraic geometry and homological algebra provide powerful tools for studying universal models of quantised integrable systems. The objective of this research program is to fullfill this study and to explore the universal modells by sheaf theoretical methods. In particular, we wish to find interactions between semi-classical analysis and standard concepts of singularity theory such as the Gauss-Manin connections, or mixed Hodge structure.

复活分析的发展为量子力学中的微扰级数提供了新的视角。这些研究反过来又引起了新的注意奇异拉格朗日品种的理论与奇异玻尔-索末菲规则。例如，问题，如收敛的系列在正规形式原来是特别感兴趣的。代数几何和同调代数的方法为研究量子化可积系统的普适模型提供了有力的工具。本研究计画的目的，是充实此一研究，并以层理论的方法来探讨普适的模型。特别是，我们希望找到半经典分析和奇点理论的标准概念之间的相互作用，如高斯-马宁连接，或混合霍奇结构。