费米开弦在B背景场中的反非对易性

Anti-noncommunitativity of Fermionic open-string in B-field Background

本文研究了B背景场中费米开弦在Neveu-Shiwarz边界条件下的反非对易性。与传统的把边界条件看作初级Dirac约束方法不同的是,为了求出场的反对易关系,首先求出场的经典解,并使用了Fadeev-Jackiw方法获得傅立叶模的对易关系。我们的结果表明,在Neveu-Shiwarz边界条件下,费米开弦在波矢空间重新分布,波矢k只能取半奇数,并且不存在零模解。这种反非对易性不仅仅是由于代数结构的要求,也是动力学的结果。

In the note, the anti-noncommutativity of an open fermionic string in the constant anti,symmetry background field under the Neveu-Shwarz boundary conditions is studied. In contrast to previous studies in which the boundary conditions （BCs） are taken as the primary Dirac constraints .In order to get the anti-non,commutative relation among the original field variables, we first get the classical solution. And the Fadeev-Jackiw method is used to obtain the commutative relation of the Fourier modes. Our result shows that the fermionic open string redistribute in wave vector space under the Neven-Shwarz boundary conditions, the wave vector k can take only the half odd numbers. We find that that the noncommutativity is not only algebraic structures but also dynamical requirements.