Faddeev-Jackiw quantization of the higher derivative Chern-Simons gauge theory in the first-order formalism

We analyse the physical constraints of the higher derivative Chern-Simons gauge model by means of Faddeev-Jackiw symplectic approach in the first-order formalism. Within such framework, we systematically determine the zero-mode structure of the corresponding symplectic matrix. In addition, we calculate the Faddeev-Jackiw quantum brackets by choosing appropriate gauge-fixing conditions and evaluate the determinant of the non-singular symplectic matrix as well as the transition-amplitude. Finally, we present a detailed Hamiltonian analysis using Dirac-Bergmann algorithm method and show that the Dirac brackets coincide with the FJ brackets when all the second-class constraints are treated as zero equations.