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arXiv · 1905.07637

The Hamilton-Jacobi analysis and Canonical Covariant description for three dimensional Palatini theory plus a Chern-Simons term

Alberto Escalante·Aldair Pantoja
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Abstract

By using the Hamilton-Jacobi [HJ] framework the three dimensional Palatini theory plus a Chern-Simons term [PCS] is analyzed. We report the complete set of $HJ$ Hamiltonians and a generalized $HJ$ differential from which all symmetries of the theory are identified. Moreover, we show that in spite of PCS Lagrangian produces Einstein's equations, the generalized $HJ$ brackets depend on a Barbero-Immirzi like parameter. In addition we complete our study by performing a canonical covariant analysis, and we construct a closed and gauge invariant two form that encodes the symplectic geometry of the covariant phase space.

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Alberto Escalante, Aldair Pantoja. 2019-05-18. The Hamilton-Jacobi analysis and Canonical Covariant description for three dimensional Palatini theory plus a Chern-Simons term. https://arxiv.org/abs/1905.07637

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