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arXiv 0712.0135hep-th
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非对易U（1）规范势的分解

Decomposition of noncommutative U(1) gauge potential

Ziyu Liu, Xiguo Lee

备注：
9 pages
发表信息：
Commun.Theor.Phys.50:943-946,2008
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摘要：

研究了非对易规范势$\hat{A_{i}}$的分解，发现它具有内部结构，即$\hat{A_{i}}$可分解为$\hat{b_{i}}$和$\hat{a_{i}}$两部分，其中$\hat{b_{i}}$满足规范变换，$\hat{a_{i}}$满足伴随变换，非对易U（1）规范势的Seiberg-Witten映射也是如此.利用Seiberg-Witten映射，构造了非对易空间与普通空间之间的单位向量场映射，发现非对易U（1）规范势及其规范场张量可以用单位向量场表示.当单位向量场无奇点时，非对易规范势和规范场张量与普通规范势和规范场张量相等。

英文摘要：

We investigate the decomposition of noncommutative gauge potential $\hat{A_{i}}$, and find it has inner structure, namely, $\hat{A_{i}}$ can be decomposed in two parts $\hat{b_{i}}$ and $\hat{a_{i}}$, here $\hat{b_{i}}$ satisfies gauge transformations while $\hat{a_{i}}$ satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U(1) gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tenser can be expressed in terms of the unit vector field. When the unit vector field has non singularity point, noncommutative gauge potential and gauge field tenser will equal to ordinary gauge potential and gauge field tenser.

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