Gauge symmetry and constraints structure for topologically massive AdS gravity: a symplectic viewpoint

By applying the Faddeev–Jackiw symplectic approach we systematically show that both the local gauge symmetry and the constraint structure of topologically massive gravity with a cosmological constant Λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda $$\end{document}, elegantly encoded in the zero-modes of the symplectic matrix, can be identified. Thereafter, via a suitable partial gauge-fixing procedure, the time gauge, we calculate the quantization bracket structure (generalized Faddeev–Jackiw brackets) for the dynamic variables and confirm that the number of physical degrees of freedom is one. This approach provides an alternative to explore the dynamical content of massive gravity models.