On the universal representation of the scattering matrix of affine Toda field theory
On the universal representation of the scattering matrix of affine Toda field theory
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DOI：
10.1016/s0550-3213(99)00578-7
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发表时间：
1999-07
期刊：
影响因子：
--
通讯作者：
A. Fring;C. Korff;B. Schulz
中科院分区：
文献类型：
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作者：
A. Fring;C. Korff;B. Schulz
利用q-变形Coxeter元的性质，可以用完全一般的方式表示任意单李代数对偶对具有实耦合常数的仿射Toda场论的散射矩阵。讨论了q-变形Coxeter元、扭曲q-变形Coxeter元和未变形Coxeter元约束态存在的控制方程，即融合规则。我们建立了这些不同公式之间的精确关系，并研究了它们的解。证明了广义s矩阵自举方程等价于融合规则。给出了不同版本的融合规则与量子守恒量之间的关系，得到了双q变形类卡坦矩阵的零向量。利用这个矩阵的性质和所谓的组合自举方程，推导出用两个对偶代数中的任意一个的量表示散射矩阵的一般积分表示。我们提供了大量的个案数据，特别是由各种考克斯特元素产生的轨道。
By exploiting the properties of q-deformed Coxeter elements, the scattering matrices of affine Toda field theories with real coupling constant related to any dual pair of simple Lie algebras may be expressed in a completely generic way. We discuss the governing equations for the existence of bound states, i.e. the fusing rules, in terms of q-deformed Coxeter elements, twisted q-deformed Coxeter elements and undeformed Coxeter elements. We establish the precise relation between these different formulations and study their solutions. The generalized S-matrix bootstrap equations are shown to be equivalent to the fusing rules. The relation between different versions of fusing rules and quantum conserved quantities, which result as nullvectors of a doubly q-deformed Cartan like matrix, is presented. The properties of this matrix together with the so-called combined bootstrap equations are utilised in order to derive generic integral representations for the scattering matrix in terms of quantities of either of the two dual algebras. We present extensive case-by-case data, in particular on the orbits generated by the various Coxeter elements.