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BRST deformations and stability in the higher derivative Chern–Simons gauge theory

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.