Symplectic Approach of Three-Dimensional Palatini Theory Plus a Chern-Simons Term

摘要

Using the symplectic framework of Faddeev-Jackiw, the three-dimensional Palatini theory plus a Chern-Simons term [P-CS] is analyzed.We report the complete set of Faddeev-Jackiw constraints and we identify the corresponding generalized Faddeev-Jackiw brackets. With these results, we show that although P-CS produces Einstein's equations, the generalized brackets depend on a Barbero-Immirzi-like parameter. In addition, we compare our results with those found in the canonical analysis showing that both formalisms lead to the same results.