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 (4)

• Canonical analysis of $n$-dimensional Palatini action without second-class constraints
• Spin connection formulations of real Lorentzian General Relativity
• Revisiting the solution of the second-class constraints of the Holst action
• Polysymplectic formulation for BF gravity with Immirzi parameter