规范变换

By using the method of the gauge transformation,this paper obtains the gauge transformation of Eigenvalue problems of energy dependent potentials and the Backlund transformation.

用规范变换的方法，导出了位势依赖于能量的特征值问题的规范变换及相应的贝克隆变换。

By making use of standard transformation and selecting proper gauge transformation conditions, I try to solve the time dependent Schringer equation and derive the exact solution. Under the population representation.

然后采用规范变换的方法，通过选取适当的规范变换条件求解含时Schrodinger方程，在粒子数表象中求得了精确解。

We construct the generator of gauge transformation and the generator of BRST transformation, then we obtain gauge transformation and BRST transformation of component fields, we find certain relations between the BRST generator and the gauge generator.

我们构造了体系的规范生成元和BRST生成元，分别得到了场量的规范变换和BRST变换，发现超对称不同场的BRST变换与规范变换存在一定的关系。

In or-der to keep the form of the Lax operator for AKNS hierarchy,there are twochoices for each type of gauge transformations,which just results in two classesof functions used to trigger the gauge transformation.

为了保持AKNS系列的Lax算子形式，两种类型规范变换都存在两种选择，这正好导致用于制作规范变换的两类函数。

Then the momentum P in the acquired motion equation is replaced by quantum operator, thus we obtain Schrodinger equation for charged particle moving in magnetic fields in Quantum Mechanics. Then we discuss the Gauge transformation and gauge invariance of Schrodinger equation, following which the Dirac phase is introduced.

然后把经典力学中的哈密顿量量子化，得到量子化的带电粒子在磁场中运动的薛定谔方程，之后是薛定谔方程的规范变换和规范不变性，并引入Dirac不可积相因子的概念。

Then we in-vest gate Seiberg-Witten map, which defines the equivalence relation of the gauge symmetries in different spaces. We also analyse the U gauge electromagnetic field in noncommutative space. Finally we discuss the ambiguities of Seiberg-Witten map, and find although that some part of the ambiguities can be absorbed by gauge transformation and hence negligible, the existence of the matter field makes some other parts difficult to be absorbed by gauge transformation or field redefinition.

然后利用Seiberg-Witten映射，我们研究了不同空间的规范对称性的等价问题，并对非对易空间的电磁场进行了微扰分析，最后我们对Seiberg-Witten映射的松动进行了讨论，研究发现这些松动中的一部分可以由规范变换吸收因而是可以忽略的，由于物质场的存在，另外一部分很难用规范变换和场的重定义吸收。

During the transition from global gauge transformation to local gauge one,field interaction undergoes a 'nothing'-to-'something' change,thus affecting gauge invariance.

当使自由粒子整体规范变换向局域规范变换过渡时，场的相互作用发生了从"无"到"有"的变化，规范不变性遭到了破坏。

For the timelike surfaces with constant positive Gaussian curvature (K=1) in R〓, we construct the correspondence between R〓 and sl (2, R), and deduce the fundamental equations for a special choice of the velocity of motion of time-like surfaces in asymptotic coordinates under suitable conditions, meanwhile, we give the B〓cklund transformation and one soliton solution of the evolution equations, then in terms of a gauge transformation we obtain the explict expression of the motion of surfaces.

对于三维Minkowski空间R〓中具有正常高斯曲率（K=1）的类时曲面，取定特定速度，在以渐近线作为坐标曲线的情况下，曲面运动满足两个基本方程，即sinh-Gordon方程和θ随时间演化的方程（其中θ表示两条渐近线之间的夹角），同时给出两个基本方程的B〓cklund变换和单孤子解，并通过规范变换给出相应的正常高斯曲率曲面的显式表达式。

By using a gauge transformation between thetwo eigenvalue problems, we obtain a correspondence between the hie -rarchy of nonlinear evolution equations associated with the Kaup-Newelleigenvalue problem and the hie rarchy of nonlinear evolution equationsassociated with the AKNS eigenvalue problem.

利用规范变换，我们得到了与Kaup-Newell特征值问题相联系的一族非线性演化方程和与AKNS特征值问题相联系的一族非线性演化方程之间的一个对应关系，并给出了Kaup-Newell系统的Darboux变换及其证明。

We also introduced the guage transformation, by this transformation, obtain the Lax equation and commutative family on the reduction space.

此外，还引入了规范变换，通过规范变换，就可以在约化相空间上得到Lax方程与对合系。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。