Barbero's formulation from a $BF$-type action with the Immirzi parameter

Abstract

Starting from a constrained real $BF$-type action for general relativity that includes both the Immirzi parameter and the cosmological constant, we obtain the Ashtekar-Barbero variables used in the canonical approach to the quantization of the gravitational field. This is accomplished by explicitly solving the second-class constraints resulting from the Hamiltonian analysis of the considered action, and later imposing the time gauge. All throughout this work the tetrad formalism is left aside, obtaining the Ashtekar-Barbero variables entirely in terms of the $B$-fields that define the action.

arXiv comment12 pages, no figures

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Cited by in corpus (6)

• $BF$ gravity
• Manifestly Lorentz-covariant variables for the phase space of general relativity
• Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes
• $SU(1,1)$ Barbero-like variables derived from Holst action
• Revisiting the solution of the second-class constraints of the Holst action
• Canonical analysis with no second-class constraints of $BF$ gravity with Immirzi parameter