The exact S-matrices of affine Toda field theories
The exact S-matrices of affine Toda field theories
复制标题
仿射户田场论的精确 S 矩阵
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
P. Dorey
中科院分区：
文献类型：
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作者：
P. Dorey
本文研究了1+1维中各种有质量场论的精确解。第一种是抽象的、非拉格朗日的，它依赖于人们对无质量二维场论的充分理解。可以发展一个微扰方案，在其中可以作出各种精确的陈述。第1章回顾了这种技术，以及在各种简单情况下应用它的一些工作。研究的特殊结构与某些李代数有着深刻的联系，这一事实将在本章的最后三节中讨论。一个补充的方法是研究特定的，经典可积的拉格朗日，希望他们的量子版本也将允许一个精确的治疗。在一定程度上受到第一章的研究结果的启发，论文的其余部分致力于一类特殊的模型，称为仿射户田场论。混合微扰和非微扰的想法。非微扰元素可以在第2章回顾的解析S-矩阵理论中找到，而微扰量子处理所需的经典理论的各种特征将在第3章中导出。利用这些信息，第4章提出了一个大子集的户田理论，然后检查微扰理论的S-矩阵的精确表达式。最后，讨论了户田S-矩阵与第一章中所研究的无质量理论微扰的相关性，并指出了今后工作的一些可能方向。
This thesis is concerned with exact solutions to various massive field theories in 1+1 dimensions.Two approaches are described. The first, abstract and non-lagrangian, relies on the considerable understanding that there now is of massless two-dimensional field theories. A perturbative scheme can be developed within which various exact statements may be made. Chapter 1 contains a review of this technique, together with some work applying it in various simple situations. The particular structures studied turn out to have a deep connection with certain Lie algebras, a fact which is discussed in the concluding three sections of the chapter. A complementary approach is to study specific, classically integrable, lagrangians in the hope that their quantum versions will also permit an exact treatment. Motivated to some extent by the findings of chapter 1, the remainder of the thesis is devoted to a particular class of models known as affine Toda field theories. Mixtures of perturbative and non-perturbative ideas are employed. The non-perturbative elements are to be found in analytic S-matrix theory, reviewed in chapter 2, while various features of the classical theory necessary for a perturbative quantum treatment are derived in chapter 3. Making use of this information, chapter 4 proposes exact expressions for the S-matrices for a large subset of the Toda theories, which are then checked in perturbation theory. Finally, the relevance or otherwise of the Toda S-matrices to the perturbations of massless theories studied in chapter 1 is discussed, and some possible directions for future work are mentioned.