The Hamilton-Jacobi analysis and canonical covariant description for three-dimensional Palatini theory plus a Chern-Simons term
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570, Puebla Pue., Mexico
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Accepted: 11 June 2019
Published online: 10 September 2019
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 despite 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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019