【作者】 王晓辉；

【导师】 侯伯宇； 岳瑞宏；

【作者基本信息】 西北大学 ， 理论物理， 2003， 硕士

【摘要】 非对易是弦理论中的重要内容。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。Witten的星乘积是不可交换的和可结合的。同时我们知道存在另外一种乘积——Moyal乘积，它是Moyal在相空间中建立起来的。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。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。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。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。最后我们运用共形映射的方法构造了费米场中的一个投影算子——蝴蝶态。更多还原

【Abstract】 String theory and noncommutative geometry are modern ideas in physics. In 1986, Witten had set up an elegant string field theory by introduce a new, beautiful approch to interactions. He had developed a new mathematical framework in terms of non-commutative differential geometry. Witten’s star is noncommutative and associative. Also, we had known another noncummutative star, Moyal product, which was defined in phase space. Recently, in his stimulating paper Bars found a map of Witten’s star to Mayol’s star. This motivated us to study the explicit relations between Witten’s star and Moyal product. 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. Fortunately we find it does not depend on the value of the B field. In addition, by using conformal field theory techniques the NS matter butterfly state is given.更多还原