规范变换

In chapter I, we introduce the Jordan-Wigner transformation in detail, and illustrate its applications with three examples: the one-dimensional S = 1 XXZ model; the bilinear-biquadratic SU(2) invariant S = 1 chain; and the ionic Hubbard chain in the strong coupling limit. In chapter II, we review the S = 1/2 transverse Ising chain in detail.

在变换后发现隐藏在自旋为1的系统里自旋为1/2的SU(2)对称性及广义的U(1)规范对称性；(3)通过将推广的强耦合极限下的一维离子型Hubbard 模型变换为SU(3)反铁磁Heisenberg 模型，严格论证了离子型Hubbard 模型从能带绝缘体到莫特绝缘体的转变区域中自发二聚化绝缘体铁电性相即键序波相的存在。

Based on the normative fractional Fourier transform and the concept of the optical transfer function, using the linear system theory, the mathematic expressions of fractional transfer function in Fresnel diffraction system and Fraunhofer diffraction system are given respectively.

基于规范光学分数傅里叶变换，从光学传递函数概念出发，根据菲涅耳衍射、夫琅和费衍射定义，应用线性系统理论，分别给出了菲涅耳与夫琅和费衍射系统在规范分数傅里叶变换下的光学传递函数数学表达式。

Two fundamental concepts are intro- duced:exact Yang-Mills equation and characteristic transformation of Yang-Mills gauge fields.

对于这种恰当的YM-方程，构造了一类线性微分变换，称之为SU(2)规范场的示性变换。

Using Lewis-Riesenfeld theory, we obtain exact solutions of the time-dependent system, then we recover both n -pulse method based on time-evolution operator of the system and STIRAP method in terms of instantaneous eigenstates with the help of time-dependent gauge transformation.

利用含时规范变换理论得到系统的精确解，我们用时间演化算符同时得到文献中分别采用π-位相法和STIRAP方法得到的结果，因而更具有普遍性。

In the case ofreflectionlessness,after determining the gauge transformation,expressions of multi-soliton solutions of the L-L equation with an easy plane are obtained explicitly bysolving the linear algebraic equations with the aid of the well-known Binet-Canchyformula.

由于要克服因Jost解在参数趋于无穷时不独立于L-L方程的解的困难，必须引进规范变换，这是不涉及微分方程的Riemann问题方法无法解决的。

Taking advantage of gauge transformation and dipolar approximation, we qualitatively derive rotating Bose-Hubbard model.Then finite temperature phase boundary between superfluid phase and normal state in rotating Bose-Hubbard model is analytically derived by studying the stability of normal state in rotating bosonic optical lattice.We also analytically prove that as the function of rotation angular velocity the oscillation of critical hopping matrix directly follows the upper boundary of Hofstadter butterfly.

4通过做一个规范变换和偶极近似，定性地推导了旋转Bose-Hubbard模型，并且通过研究正常态不动点的稳定性推广了旋转Bose-Hubbard模型的零温相图到有限温度的情形；另外根据系统有效的能带宽度与旋转速度的关系(Hofstadter蝴蝶)，得到了系统的临界跃迁矩阵随旋转速度的改变展示谐振行为的结论。

To overcome the difficulty caused by the fact that the Lax pair depends on thesolution of the equation as |k|→∞,we write the Darboux matrix with N-poles inthe form:〓,where factor 〓 is a gauge transformation which isindepent from k and 〓 tends to the unit-matrix I as |k|→∞.

为了克服当|k|→∞时，Lax对仍依赖于方程的解所引起的困难，我们把含N对极点的Darboux矩阵〓分解为两部分：〓，其中〓为与参数k无关的2×2矩阵，它相当于一个规范变换。而〓当|k|→∞时趋于单位矩阵I。

In this paper, the author introduces component and OpenGIS including the specification of Spatial Reference System Components —Interfaces and Classes. After analyzing and comparing several methods of map projection transformation, the author chooses the inverse transformation method as the main one.

本文首先介绍了组件技术和OpenGIS规范及其有关空间参照系统的接口和组件对象的定义，在对几种地图投影变换方法进行分析比较之后，选择反解变换法作为主要方法。

Two fundamental concepts are introduced:exact Yang-Mills equation and characteristic transformation of Yang- Mills gauge fields.

然后构造了一类线性微分变换，称之为SU(3)规范场的示性变换，它具体给出联络和截面之间的微分关系。

Based on the phase-space generating functional for a system with a singular higher-order Lagrangian,the quantal canonical Noether identities under the local and non-local transformation in phase space for such system have been derived.

基于高阶微商奇异拉氏量系统的相空间生成泛函，导出了定域和非定域变换下的量子正则Noether恒等式；对高阶微商规范不变系统，导出了位形空间中定域和非定域变换下的量子Noether恒等式。

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。