On the Faddeev-Jackiw Symplectic Framework for Topologically Massive Gravity

TL;DR

This paper applies the Faddeev-Jackiw symplectic approach to topologically massive gravity, simplifying the analysis of constraints and gauge symmetries compared to the traditional Dirac method.

Contribution

It demonstrates how the Faddeev-Jackiw method can efficiently determine constraints and gauge generators in topologically massive gravity, avoiding ambiguities of the Dirac formalism.

Findings

Complete set of constraints obtained

Gauge symmetry generators identified

Advantages over Dirac formalism discussed

Abstract

The dynamical structure of topologically massive gravity in the context of the Faddeev-Jackiw symplectic approach is studied. It is shown that this method allows to avoid some ambiguities arising in the study of the gauge structure via the Dirac formalism. In particular, the complete set of constraints and the gauge symmetry generators of the theory are obtained straightforwardly via the zero-modes of the symplectic matrix. In order to obtain the generalized Faddeev-Jackiw brackets and calculate the local physical degrees of freedom of this model, an appropriate gauge-fixing procedure is introduced. Finally, the similarities and advantages between Faddeev-Jackiw method and Dirac's formalism are briefly discussed.