摘要
在这份报纸，我们在 noncommutative 数量模型把我们的最近的工作的假设用于 noncommutative U (1 ) 计量器理论。这个假设是 noncommutative 效果开始从规模 NC 连续地是可见的并且在这规模下面，理论是可交换的。把假设和使用的背景领域方法和环计算基于这，一个有效行动为 noncommutative U (1 ) 被导出计量器理论。这将被显示出有效理论是的相应低精力 asymptotically 自由并且在这下面调节 noncommutative 二次的红外分叉不出现。有效理论包含更高维的条款，它在高精力变得更重要。这些条款预言由于空间的 noncommutativity 散布的一个有弹性的光子光子。这些更高维的条款的系数也满足显示在这个理论， superluminal 的相关疾病发信号宣传， S 矩阵的坏分析性质不存在的确实限制。在最后节，我们将把我们的方法用于 noncommutative 额外的尺寸理论。
In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U（1） gauge theories. This assumption is that the noneommutative effects start to be visible continuously from a scale ANC and that below this scale the theory is a commutative one. Based on this assumption and using background field method and loop calculations, an effective action is derived for noncommutative U（1） gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. The coefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.
