RUI: Applications of Supersymmetry to Quantum Mechanics

PI:Donald Spector研究所：Hobart and William Smith College PHY 0457048标题RUI：超对称在量子力学中的应用PI将继续他正在进行的具有中心电荷的超对称量子力学的研究。他将探索这些系统表现出目标空间对偶性所必需的性质，通过结合手性超场、新的目标空间流形和依赖费米子场的中心电荷来扩展他以前的工作。超代数、中心电荷和对偶在流线型环境中的关系的研究将提供对场论和弦理论行为的洞察。形状不变性，一种理解完全可溶系统的强大技术，已经被PI证明具有BPS (Bogomol？nyi-Prasad-Sommerfield)配方。基于这一点以及BPS现象与拓扑孤子之间已建立的联系，PI将识别在拓扑非平凡背景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的形状不变性模型的识别。他将从一维扩展到高维，利用部分超对称来寻找量子哈密顿量的渐近能级分布。这将阐明量子混沌中关于二维系统中能级统计的猜想。

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.