Lagrangian and Hamiltonian formulations of higher order Chern-Simons theories

We consider models involving the higher (third) derivative extension of the Abelian Chern-Simons (CS) topological term in D = 2 + 1 dimensions. The polarization vectors in these models reveal an identical structure with the corresponding expressions for usual models which contain, at most, quadratic structures. We also investigate the Hamiltonian structure of these models and show how Wigner's little group acts as a gauge generator.