标题： 与无限Weyl群相关的Toda场理论和Calogero模型 显示英文标题

标题： Toda field theories and Calogero models associated to infinite Weyl groups

摘要： 许多可积理论可以统一地用李代数根系来表述。 研究得较为透彻的是符合不变的标量场理论的Toda型及其质量版本，它们分别可以用有限李代数和仿射Kac-Moody代数的简单根来表示。 此外，需要整个根系来表述的Calogero-Moser-Sutherland型多粒子系统也得到了广泛研究。 在这里，我们讨论最近提出的这些模型向基于双曲和洛伦兹Kac-Moody代数的类似系统的扩展。 我们探讨了这些模型的各种性质，包括它们的可积性以及它们相对于仿射、双曲和洛伦兹类型无限Weyl群的不变性。 显示英文摘要

摘要： Many integrable theories can be formulated universally in terms of Lie algebraic root systems. Well-studied are conformally invariant scalar field theories of Toda type and their massive versions, which can be expressed in terms of simple roots of finite Lie and affine Kac-Moody algebras, respectively. Also, multi-particle systems of Calogero-Moser-Sutherland type, which require the entire root system in their formulation, are extensively studied. Here, we discuss recently proposed extensions of these models to similar systems based on hyperbolic and Lorentzian Kac-Moody algebras. We explore various properties of these models, including their integrability and their invariance with respect to infinite Weyl groups of affine, hyperbolic, and Lorentzian types.