Lagrangian and Hamiltonian formulations of higher order Chern-Simons theories

TL;DR

This paper explores higher derivative extensions of abelian Chern-Simons theories in 2+1 dimensions, analyzing their polarization vectors and Hamiltonian structure, including the role of Wigner's little group as a gauge generator.

Contribution

It introduces the Hamiltonian formulation of third-derivative Chern-Simons models and reveals the gauge-generating role of Wigner's little group in these higher-order theories.

Findings

Polarization vectors have identical structure to standard models.

Hamiltonian analysis shows Wigner's little group acts as a gauge generator.

Higher derivative models maintain topological features with extended structures.

Abstract

We consider models involving the higher (third) derivative extension of the abelian Chern-Simons (CS) topological term in D=2+1 dimensions. The polarisation 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 gauge generator.