Canonical analysis of $n$-dimensional Palatini action without second-class constraints

Abstract

We carry out the canonical analysis of the $n$-dimensional Palatini action with or without a cosmological constant $(n\ge 3)$ introducing neither second-class constraints nor resorting to any gauge fixing. This is accomplished by providing an expression for the spatial components of the connection that allows us to isolate the nondynamical variables present among them, which can later be eliminated from the action by using their own equation of motion. As a result, we obtain the description of the phase space of general relativity in terms of manifestly $SO(n-1,1)$ [or $SO(n)$] covariant variables subject to first-class constraints only, with no second-class constraints arising during the process. Afterwards, we perform, at the covariant level, a canonical transformation to a set of variables in terms of which the above constraints take a simpler form. Finally, we impose the time gauge and make contact with the $SO(n-1)$ ADM formalism.

arXiv commentPaper's title was changed, expanded analysis, notation was changed a bit, added reference, corrected typos

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• Straightforward Hamiltonian analysis of $BF$ gravity in $n$ dimensions
• Canonical quantization for Equilibrium Thermodynamics
• Hamiltonian gravity in tetrad-connection variables
• Fermions coupled to the Palatini action in $n$ dimensions
• Barbero-Immirzi connections and how to build them
• Canonical analysis of $BF$ gravity in $n$ dimensions
• Generators of Local Lorentz Transformation in ADM-Vielbein Formalism of Gravitational Relativity