Geometry and dynamics of integrable systems with extended supersymmetry

具有扩展超对称性的可积系统的几何和动力学

• 批准号: 429770112
• 负责人: Professor Dr. Olaf Lechtenfeld
• 金额: --
• 依托单位: Joint Institute for Nuclear Research (JINR)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/429770112?language=en
• 关键词: Geometry; dynamics; integrable; systems; extended

The project focuses on integrable systems which possess additional symmetries such as conformal symmetry or/and extended supersymmetry. New multi-particle rational, trigonometric and hyperbolic Calogero systems associated with the A(n), B(n), C(n) and D(n) Lie algebras with an arbitrary even number of supersymmetries will be constructed and analyzed within the Hamiltonian approach. The superconformal symmetries of these models will be visualized by an explicit construction of the corresponding conserved currents. Calogero systems associated with the exceptional G(2) and F(4) algebras and possessing N-extended supersymmetry will be constructed and analyzed. A superfield description of these models with N=2 and N=4 supersymmetry will be provided. For a large class of integrable models, N=2 and N=4 supersymmetric extensions will be constructed and investigated. This includes Ruijsenaars-Schneider systems, Schwarzian mechanics, Euler, Lagrange, Kovalevskaya and Goryachev-Chaplygin tops, multi-vortices on the plane, and su(2) mechanics associated with the angular sector of a relativistic spinning particle on a spherically symmetric gravitational background.

该项目侧重于具有额外对称性的可积系统，如共形对称或/和扩展超对称。本文将在哈密顿方法中构造和分析具有任意偶数超对称性的A(n)、B(n)、C(n)和D(n)李代数相关的新的多粒子有理、三角和双曲卡罗热罗系统。这些模型的超共形对称性将通过相应的守恒电流的显式构造来可视化。构造并分析了具有n扩展超对称的特殊G(2)和F(4)代数的Calogero系统。给出了N=2和N=4超对称模型的超场描述。对于一类大的可积模型，构造并研究了N=2和N=4的超对称扩展。这包括rujsenaars - schneider系统，Schwarzian力学，欧拉，拉格朗日，Kovalevskaya和Goryachev-Chaplygin顶，平面上的多涡旋，以及与球对称引力背景下相对论性自旋粒子的角扇区相关的su(2)力学。