| 1. | Witten ' s star is noncommutative and associative
Witten的星乘积是不可交换的和可结合的。 |
| 2. | This motivated us to study the explicit relations between witten ' s star and moyal product
这就促使我们进一步来研究witten的星乘积和moyal乘积之间的关系。 |
| 3. | Recently , in his stimulating paper bars found a map of witten ' s star to mayol ' s star
最近bars的研究工作表明在弦理论中这两种非对易乘法是等价的，它们之间可以通过一个映射联系起来。 |
| 4. | In 1986 , witten had set up an elegant string field theory by introduce a new , beautiful approch to interactions
1986年witten建立了三弦场论，引入了非对易的乘法来实现弦场论中的基本相互作用。 |
| 5. | It is shown that vector boson have a mass generation and the effective lagrangian contains a term corresponding to the a wess - zumino - witten like term , which was consistant with noncommutative chiral schwinger model
在非阿贝尔情形，我们发现在它的有效拉氏量中矢量玻色子有质量生成，有效作用量里包含wess - zumino - witten项。 |
| 6. | In this paper , we recast the matter part of the open superstring star in the present of a constant b field . by using a different coordinate representation the matter part of the open superstring star is identified with the continuous mayal product of functions of anti - commuting variables
在本文中，我们着重考察了在背景b场中费米场中的witten星乘积，将其表示为连续的moyal乘积，并且定出了非对易的参数。 |
| 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. | Witten ' s open string field theory formulate the interaction of bosonic open strings in the language of noncommutative geometry . compactification of matrix theory on the noncommutative torus was argued to correspond to supergravity with constant background three form tensor field . more generally , it has been realised that noncommutative gauge theory arises in the worldvolume theory on d - brane in the presence of a constant background b field in string theory
Witten的开弦场论用非对易几何描述了玻色开弦的相互作用；在非对易torus上的矩阵理论的紧化对应于带有常数三形式张量场的超引力；更为普遍的，非对易规范理论可以自然地产生在带有常数b背景场的三维d - brane上。 |
