论文标题
在非常特殊的相对论中诱导非亚伯式的Chern-Simons有效的行动
Induced non-Abelian Chern-Simons effective action in very special relativity
论文作者
论文摘要
在本文中，我们研究了在$（2+1）$ - 维度时空中，在非常特殊的相对论（VSR）框架中对非亚伯仪场的一环诱导作用。我们表明，有新的图表有助于Gluon $ n $ Point函数的振幅，例如$ \ langle gg \ rangle $，$ \ langle ggg \ rangle $和$ \ langle gggg \ rangle $，源自VSR中生成的非本地耦合。使用相关图的一环分析，我们将VSR校正评估为三个维度的非亚伯仪场作用的诱导动力学项。接下来，通过应用病房身份，我们确定$ \ langle gg \ rangle $在VSR中的振幅的一般紧张结构，这在循环分析的任何顺序上都是有效的。此外，我们通过分析$ \ langle gg \ rangle $，$ \ langle ggg \ rangle $和$ \ langle gggg \ rangle $，讨论对非亚洲Chern-Simons和Yang-Mills Action的领先VSR校正。为了突出VSR效应，我们介绍了非亚伯式Chern-Simons有效作用的VSR修改，然后获得非亚伯仪场的运动方程。结果，我们观察到，在存在VSR效应的情况下，众所周知的纯量规溶液不存在。
In this paper, we study the one-loop induced effective action for a non-abelian gauge field in the very special relativity (VSR) framework in a $(2+1)$-dimensional spacetime. We show that there are new graphs contributing to the amplitudes of gluon $n$-point functions, e.g. $\langle GG\rangle$, $\langle GGG \rangle$ and $\langle GGGG \rangle$, originating from the non-local couplings generated in VSR. Using the one-loop analysis of the relevant graphs, we evaluate the VSR corrections to the induced kinetic term of the non-abelian gauge field action in three dimensions. Next, by applying the Ward identity, we determine the general tensorial structure for the amplitude of $\langle GG\rangle$ in VSR, which is valid at any order of the loop analysis. Moreover, we discuss the leading VSR corrections to the non-abelian Chern-Simons and Yang-Mills action through the analysis of $\langle GG\rangle$, $\langle GGG \rangle$ and $\langle GGGG \rangle$. In order to highlight the VSR effects, we present the VSR modification of non-abelian Chern-Simons effective action and then obtain the equation of motion for the non-abelian gauge field. As a result, we observe that the well-known pure gauge solution does not hold in the presence of VSR effects.
