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

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 so...

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Bibliographic Details
Published in:Classical and quantum gravity 2016-06, Vol.33 (11), p.115014
Main Authors: Celada, Mariano, Montesinos, Merced, Romero, Jorge
Format: Article
Language:English
Subjects:
BF gravity
canonical general relativity
Immirzi parameter
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Summary: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.
ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/33/11/115014