具有O（d）对称群的非线性西格玛模型的推广在约束链动力学中的应用
Applications of a generalization of the nonlinear sigma model with O(d) group of symmetry to the dynamics of a constrained chain
摘要：
本文的主要工作是将场论模型（这里称为广义非线性西格玛模型或简称GNLSM）应用于受约束的链的动力学。Edwards和Goodyear在一篇开创性的论文中使用基于Langevin方程的方法讨论了具有相似属性和约束的链。GNLSM已经在以前的出版物中提出，以描述一个二维链的动力学。本文将该模型推广到d维，并在其作用量中加入了弯曲能项。作为应用，计算了两个观测量的情况下，一个非常刚性的链。第一个可观察的是环形链的动态形状因子。第二个可观察到的是对静态形状因子的动态的直接概括。这个观测值是相关的，以便估计链上任意两点之间的平均距离。最后，GNLNM的一个变种，其中的拓扑条件，约束的运动的两个链接链的高斯链接不变量的帮助下施加。
英文摘要：
Subject of this work are the applications of a field theoretical model, called here generalized nonlinear sigma model or simply GNLSM,to the dynamics of a chain subjected to constraints. Chains with similar properties and constraints have been discussed in a seminal paper of Edwards and Goodyear using an approach based on the Langevin equation. The GNLSM has been proposed in a previous publication in order to describe the dynamics of a two dimensional chain. In this paper the model is extended to d dimensions and a bending energy term is added to its action. As an application, two observables are computed in the case of a very stiff chain. The first observable is the dynamical form factor of a ring shaped chain. The second observable is a straightforward generalization to dynamics of the static form factor. This observable is relevant in order to estimate the average distance between two arbitrary points of the chain. Finally, a variant of the GNLNM is presented, in which the topological conditions which constrain the motion of two linked chains are imposed with the help of the Gauss linking invariant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
