贝雷津量子化,符合性接和博特-维拉索罗集团
A Alekseev1, S Shatashvili2,3,4, L Takhtajan5,6
1Section of Mathematics, University of Geneva, Rue du Conseil Général 7-9, 12211 Geneva, Switzerland.
概括
我们用希尔伯特空间上的运算符表示量化了符合性接. 这就产生了一个新的可循环级别代表,并为塔赫塔扬-泰奥能源功能提供了一个令人惊的身份.
科学领域:
- 数学物理 数学物理
- 代表理论 代表理论
- 复杂分析 复杂分析
背景情况:
- 这项研究建立在Nag-Sullivan框架上,用于表示圆形二形态的组.
- 它探讨了全方位函数的希尔伯特空间及其与simplectic转换的联系.
- 符合接是提供三角分解的关键概念.
研究的目的:
- 在希尔伯特空间上研究圆的二元形态群的表示.
- 使用操作员形式主义量化符合性接的概念.
- 寻找Bott-Virasoro可自行车级别的新代表,并探索能源功能.
主要方法:
- 利用贝雷津形式主义,将分解提升到对福克空间起作用的操作者.
- 在宏观函数的希尔伯特空间上应用运算子理论.
- 分析从合规接中衍生出来的simplectic转换.
主要成果:
- 这样可以成功地实现对合规接的量化.
- 识别了Bott-Virasoro自行车级别的新型代表.
- 在圆上,我们得出了塔赫塔扬-泰奥能量函数的令人惊的同一性.
结论:
- 运算子理论方法为研究符合性场理论和相关领域提供了一个强大的工具.
- 这些发现为博特-维拉索罗共循环和能量功能的结构提供了新的见解.
- 这项工作将表征理论,复杂分析和数学物理学的概念联系起来.
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