孤立子理论中群流形上的自洽场方法和$τ$泛函方法：回顾和新结果
Self-Consistent-Field Method and $τ$-Functional Method on Group Manifold in Soliton Theory: a Review and New Results
摘要：
最大解耦方法被认为是一种将可积性条件的基本思想应用于某些多重参数化对称的理论。该方法被看作是描述集合子流形对称性的一种数学工具，其中正则性条件使集合变量成为一个正交坐标系。为了这个目的，我们采用了一个概念的曲率不熟悉的传统的时间相关（TD）的自洽场（SCF）理论。我们的基本思想是引入一种与流体动力学相似的拉格朗日方式来描述集体坐标系。这种方式使我们能够采取一种形式，它是线性组成的TD SCF哈密顿量和无穷小生成元诱导的集体变量微分的正则变换的群。系统的可积性条件为曲率C=0。我们的方法被构造成显示所考虑的组的结构。>...
英文摘要：
The maximally-decoupled method has been considered as a theory to apply an basic idea of an integrability condition to certain multiple parametrized symmetries. The method is regarded as a mathematical tool to describe a symmetry of a collective submanifold in which a canonicity condition makes the collective variables to be an orthogonal coordinate-system. For this aim we adopt a concept of curvature unfamiliar in the conventional time-dependent (TD) self-consistent field (SCF) theory. Our basic idea lies in the introduction of a sort of Lagrange manner familiar to fluid dynamics to describe a collective coordinate-system. This manner enables us to take a one-form which is linearly composed of a TD SCF Hamiltonian and infinitesimal generators induced by collective variable differentials of a canonical transformation on a group. The integrability condition of the system read the curvature C=0. Our method is constructed manifesting itself the structure of the group under consideration. >...
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