论文标题
真正的汉密尔顿形式的仿射托达田间理论：光谱方面
Real Hamiltonian forms of affine Toda field theories: spectral aspects
论文作者
论文摘要
该论文致力于与特殊简单的谎言代数相关的二维TODA场理论的真实汉密尔顿形式，以及相关的Lax运算符的光谱理论。真正的汉密尔顿形式是汉密尔顿系统的一种特殊类型的“减少”，类似于真实形式的半简单代数代数。研究了与特殊复杂的非偏见仿射Kac-Moody代数相关的真实汉密尔顿形式的仿射TODA场理论的例子。除了相关的LAX表示外，我们还提出了相关的Riemann-Hilbert问题，并得出了最小的散射数据集，这些数据量确定了散射矩阵和LAX算子的电位。
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.
