标题： 实哈密顿形式的仿射托达场理论：谱方面 显示英文标题

标题： Real Hamiltonian forms of affine Toda field theories: spectral aspects

摘要： 本文致力于与例外简单李代数相关的二维Toda场理论的实哈密顿形式，以及相关Lax算子的谱理论。 实哈密顿形式是哈密顿系统的一种特殊类型的"约化"，类似于半单李代数的实形式。 研究了与例外复未扭仿李代数相关的仿射Toda场理论的实哈密顿形式的例子。 除了相关的Lax表示外，我们还提出了相关的黎曼-希尔伯特问题，并推导出确定Lax算子的散射矩阵和势的最小散射数据集。 显示英文摘要

摘要： The paper is devoted to real Hamiltonian forms of 2-dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax operators. Real Hamiltonian forms are a special type of "reductions" of Hamiltonian systems, similar to real forms of semi-simple Lie algebras. Examples of real Hamiltonian forms of affine Toda field theories related to exceptional complex untwisted affine Kac-Moody algebras are studied. Along with the associated Lax representations, we also formulate the relevant Riemann-Hilbert problems and derive the minimal sets of scattering data that determine uniquely the scattering matrices and the potentials of the Lax operators.