Manifestly Lorentz-covariant variables for the phase space of general relativity

Abstract

We present a manifestly Lorentz-covariant description of the phase space of general relativity with the Immirzi parameter. This formulation emerges after solving the second-class constraints arising in the canonical analysis of the Holst action. We show that the new canonical variables give rise to other Lorentz-covariant parametrizations of the phase space via canonical transformations. The resulting form of the first-class constraints in terms of new variables is given. In the time gauge, these variables and the constraints become those found by Barbero.

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References in corpus (4)

• Black hole state counting in Loop Quantum Gravity: A number theoretical approach
• $BF$ gravity
• Towards Loop Quantum Gravity without the time gauge
• Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter

Cited by in corpus (10)

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• Polysymplectic formulation for BF gravity with Immirzi parameter
• Hamiltonian analysis of fermions coupled to the Holst action
• Linking the ADM formulation to other Hamiltonian formulations of general relativity
• Generators of Local Lorentz Transformation in ADM-Vielbein Formalism of Gravitational Relativity
• Canonical analysis of $BF$ gravity in $n$ dimensions