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

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  • Alberto Escalante
  • Prihel Cavildo-Sánchez

Abstract

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.

Suggested Citation

  • Alberto Escalante & Prihel Cavildo-Sánchez, 2018. "Symplectic Approach of Three-Dimensional Palatini Theory Plus a Chern-Simons Term," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-7, March.
    • Handle: RePEc:hin:jnlamp:3474760
    DOI: 10.1155/2018/3474760
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