| 1. | The physical origin of the gauge transformation is a mystery .
这个规范变换的物理起因还是个谜。 |
| 2. | For some quintic derivative nonlinear schrodinger ( qds ) equation , kundu had shown their integrability through gauge transformations
对于某些既有五次项又有导数项的nls方程， kundu等利用规范变换得到了它们的可积性。 |
| 3. | We found the generators g of an local elliptic su ( ri ) g ( su ( n ) ) , which transform covariantly by the global gauge transformation of an - by acting on hn we establish the isomorphism of an and ? ,
此外，我们还发现了局部椭圆su ( n )代数g的生成元g ，它是按a _ n的整体规范变换进行协变变换的。作用在h _ n上，我们建立了a _ n和g之间的同构关系。 |
| 4. | An n - fold darboux transformation with multi - parameters for coupled nonlinear evolution equation of multi - component hierarchy is set up with the help of a gauge transformation of the spectral problem , from which the exact solutions of the nonlinear equations are given
摘要利用等谱问题的规范变换，为一对耦合的非线性演化方程建立了一个具有多个参数的n -波达布变换，进而求出了该方程的精确解。 |
| 5. | 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-位相法和stirap (受激拉曼散射)方法得到的结果，因而更具有普遍性。 |
| 6. | We examin e the generation of bell state in bose - einstein condensates of two interacting species trapped in a double - well configuration analytically and the density of probability for finding the entangled bell state is given . we find that the oscillation amplitude of the probability of density for finding the entangled bell state becomes greater as the ratio of the interspecies interaction strength and the tunneling rate increases , moreover the self - interaction strength of the component a ( b ) has no effect on it . also we use the time - dependent su ( 2 ) gauge transformation to diagonalize the hamilton operator , obtain the berry phase and analytically the time - evolution operator
此外我们还研究了在双阱玻色-爱因斯坦凝聚中纠缠态的演化，研究发现随着组分间相互作用和随穿率的比值的增加系统演化到bell态的概率变大，而且组分自身内在的相互作用对形成bell态的几率没有影响；并且用含时su ( 2 )规范变换对角化哈密顿量得到了系统的berry位相和时间演化算符，并研究了量子随穿过程。 |
| 7. | 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 ( l ) 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。 |
| 8. | Thereafter , we summarize the intrinsic properties of brst transformation , the canonical ward identities of phase space and the gauge generators , further sum up the first - class & the second - class constrains ( in hamiltonian system ) and the relations between the first constraints and gauge transformation generators
进而综述了brst变换的内秉性、相空间变换的正则ward恒等式和规范生成元，综合地讨论了约束hamilton系统中第一类约束和第二类约束以及第一类约束与规范变换生成元的关系。 |
