$SU(1,1)$ Barbero-like variables derived from Holst action

Abstract

We work on a spacetime manifold foliated by timelike leaves. In this setting, we explore the solution of the second-class constraints arising during the canonical analysis of the Holst action with a cosmological constant. The solution is given in a manifestly Lorentz-covariant fashion, and the resulting canonical formulation is expressed using several sets of real variables that are related to one another by canonical transformations. By applying a gauge fixing to this formulation, we obtain a description of gravity as an $SU(1,1)$ gauge theory that resembles the Ashtekar-Barbero formulation.

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Cited by in corpus (8)

• 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
• Revisiting the solution of the second-class constraints of 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
• SU(2) and SU(1,1) Y-Maps in Loop Quantum Gravity
• Hamiltonian and Diffeomorphism Constraints Generalized for Timelike and Spacelike 3+1 Foliation