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arXiv · 1605.01125

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

Mariano Celada·Merced Montesinos·Jorge Romero
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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.

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Mariano Celada, Merced Montesinos, Jorge Romero. 2016-05-04. Barbero's formulation from a $BF$-type action with the Immirzi parameter. https://doi.org/10.1088/0264-9381%2F33%2F11%2F115014

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