Indeed , noncommutative geometry has arisen in at least three distinct but closely related contexts in string theory 实际上在弦理论中，非对易几何自然地出现在至少三种不同而又密切相关的背景里。
We disscuss the field theory in noncommutative space . the gauge invariance of noncommutative gauge field coupled with matter field is studied 我们讨论了非对易空间与规范场耦合的物质场的规范对称性。
He proved the existence of nontrivial projection operators and explicitly presented an example with trace 1 / q for q an integer in z4 case 他明确给出了一个具有氛对称性不可对易orbifoldtz / g上的投影算子。
The polyamide to easy generation salivate ( pa ) , through choosing form of a powerful person hot nozzle also can realize hot flow path to shape 对易产生流涎的聚酰胺( pa ) ，通过选用阀式热喷嘴也能实现热流道成型。
Maintenance and replacement of expendable equipment components , e . g . purification filters , should be based on the results of monitoring and validation 对易耗件的维修和更换，如净化过滤器，应根据相应的监控和验证结果进行。
Martinec and moore discussed how d - branes on orbifolds fit naturally into the algebraic framework as described by projection operators Martinec和moore讨论了d一branes上的物理如何自然地与一些非对易orbifolds上的投影算子相联系。
Fortunately we find it does not depend on the value of the b field . in addition , by using conformal field theory techniques the n s matter butterfly state is given 我们发现当背景b场趋于零时，费米场中的非对易参数和玻色场中的一样。
Noncommutative field theory is a quantum field theory on noncommutative space and means that fields are thoughts of as function over noncommutative space 非对易场论是建立在非对易空间上的量子场论，它意味着场量可以看作非对易空间的函数。
One would like to know to which extent properties of quantum field theories on commutative spaces also arise in quantum field theories on noncommutative space 我们总是想知道对易空间的量子场论的特点在多大程度上同样适用于非对易空间的量子场论。
On rail security , still cited by lawmakers as the most vulnerable part of the transportation system , 13 . 2 million dollars goes for inspectors and explosive detection 在铁路安全方面，立法者将其称为交通运输最易受攻击的部分， 1320万美圆将用于增设检查人员及对易爆物品的检查。
