We establish the extended BRST and anti-BRST transformations for non-Abelian relativistic self-dual Chern–Simons theory coupled to scalar fields within the Batalin–Vilkovisky framework. Based on these constructions, we describe the total effective extended BRST-invariant Lagrangian density of the coupling theory by means of superfields with one Grassmann coordinates. Moreover, we need two fermionic variables to reexpress the extended BRST–anti-BRST-invariant Lagrangian in the superspace.

中文翻译：

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非阿贝尔自对双Chern-Simons耦合理论中的扩展BRST-反BRST变换

我们为非阿贝尔相对论自对偶陈恩·西蒙斯理论建立了扩展的BRST和反BRST变换，并与Batalin-Vilkovisky框架内的标量场耦合。基于这些构造，我们通过具有一个格拉斯曼坐标的超场描述了耦合理论的总有效扩展BRST不变拉格朗日密度。此外，我们需要两个费米子变量来重新表达超空间中扩展的BRST –反BRST不变拉格朗日方程。