RUI: Applications of Supersymmetry to Quantum Mechanics

RUI：超对称性在量子力学中的应用

• 批准号: 0457048
• 负责人: Donald Spector
• 金额: $ 6万
• 依托单位: Hobart and William Smith Colleges
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-02-15 至 2009-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0457048&HistoricalAwards=false
• 关键词: RUI; Applications; Supersymmetry; Quantum; Mechanics

Abstract PI:Donald Spector Institution: Hobart and William Smith College PHY 0457048 TITLE RUI: Applications of Supersymmetry to Quantum Mechanics The PI will continue his ongoing investigation of supersymmetric quantum mechanics with a central charge. He will explore the properties necessary for such systems to exhibit target space dualities, extending his previous work by incorporating chiral superfields, new target spacemanifolds, and central charges that depend on fermionic fields. This study of the relations among superalgebras, central charges, and dualities in a streamlined setting will provide insight into the behavior of field theories and string theory. Shape invariance, a powerful technique for understanding exactly soluble systems, has beens shown by the PI to have a BPS (Bogomol?nyi-Prasad-Sommerfield) formulation. Based on this and the established connection between BPS phenomena and topological solitons, the PI will identify specific models in which shape invariance emerges in the presence of a topologically non-trivial background, leading to a geometrical interpretation of shape invariance and the identification of new shape invariant models.. He will extend from one to higher dimensions the use of partial supersymmetry to find asymptotic energy level distributions of quantum Hamiltonians. This should shed light on conjectures in quantum chaos regarding the statistics of energy levels in two-dimensional systems.

摘要PI：Donald Spector机构：霍巴特和威廉史密斯学院物理0457048标题RUI：应用超对称量子力学的PI将继续他正在进行的研究超对称量子力学与中心电荷。他将探索这些系统表现出目标空间对偶性所必需的属性，通过将手征超场，新的目标空间流形和依赖于费米子场的中心电荷扩展他以前的工作。这种对超代数、中心荷和对偶之间关系的研究，将为理解场论和弦论的行为提供帮助。形状不变性，一个强大的技术，用于了解完全可溶性系统，已被证明是由PI有一个BPS（Bogomol？nyi-Prasad-Sommerfield）公式。基于此以及BPS现象和拓扑孤子之间建立的联系，PI将识别在拓扑非平凡背景存在下出现形状不变性的特定模型，从而导致形状不变性的几何解释和新形状不变模型的识别。他将从一维扩展到更高的维度，使用部分超对称来寻找量子哈密顿的渐近能级分布。这将有助于阐明量子混沌中关于二维系统能级统计的理论。