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By applying the Faddeev-Jackiw symplectic approach we systematically showthat both the local gauge symmetry and the constraint structure oftopologically massive gravity with a cosmological constant $\Lambda$, elegantlyencoded in the zero-modes of the symplectic matrix, can be identified.Thereafter, via an appropriate partial gauge-fixing procedure, the time gauge,we calculate the quantization bracket structure (generalized Faddeev-Jackiwbrackets) for the dynamic variables and confirm that the number of physicaldegrees of freedom is one. This approach provides an alternative to explore thedynamical content of massive gravity models.

Gauge symmetry and constraints structure in topologically massive AdS gravity: A symplectic viewpoint