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.

arXiv commentIt matches published version

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Cited by in corpus (17)

• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Canonical analysis of $n$-dimensional Palatini action without second-class constraints
• Canonical analysis of Holst action without second-class constraints
• Concise symplectic formulation for tetrad gravity
• Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action
• Covariant Origin of the $U(1{)}^3$ model for Euclidean Quantum Gravity
• Spin connection formulations of real Lorentzian General Relativity
• $SU(1,1)$ Barbero-like variables derived from Holst action
• Revisiting the solution of the second-class constraints of the Holst action
• The gauge symmetries of first-order general relativity with matter fields
• Polysymplectic formulation for BF gravity with Immirzi parameter
• Hamiltonian analysis of fermions coupled to the Holst action
• Euclidean self-dual gravity: Ashtekar variables without gauge fixing
• Canonical analysis with no second-class constraints of $BF$ gravity with Immirzi parameter
• 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