We show the procedure of BRST deformations of the free Chern–Simons gauge theory with the higher derivatives in antifield formalism and obtain the consistent interactions in the master action at different orders. The key ingredient in our analysis is the local BRST-cohomology which plays a crucial role in the determination of the first-order deformation, also the Jacobi identity is needed since it will greatly simplify the calculations for us. Making using of the Dirac’s method, we give a detailed Hamiltonian analysis both for the free and interacting systems and exhibit that the number of physical degrees of freedom is unchanged after the deformation process. Moreover, we demonstrate that the free higher derivative system can be stabilized from the viewpoint of the existence of another bounded conserved quantities which are different from the canonical energy.

我们用反场形式主义中的高阶导数显示了自由Chern-Simons规范理论的BRST变形过程，并获得了在主动作中以不同顺序的一致相互作用。我们分析的关键要素是局部BRST同构性，它在确定一阶变形中起着至关重要的作用，还需要Jacobi身份，因为它将大大简化我们的计算。利用狄拉克（Dirac）方法，我们对自由系统和相互作用系统进行了详细的汉密尔顿分析，并显示出变形后物理自由度的数量保持不变。而且，