Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 103, 13 pages      arXiv:1111.2671
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

Equivalent and Alternative Forms for BF Gravity with Immirzi Parameter

Merced Montesinos and Mercedes Velázquez
Departamento de Física, Cinvestav, Instituto Politécnico Nacional 2508, San Pedro Zacatenco, 07360, Gustavo A. Madero, Ciudad de México, México

Received August 31, 2011, in final form November 07, 2011; Published online November 11, 2011

A detailed analysis of the BF formulation for general relativity given by Capovilla, Montesinos, Prieto, and Rojas is performed. The action principle of this formulation is written in an equivalent form by doing a transformation of the fields of which the action depends functionally on. The transformed action principle involves two BF terms and the two Lorentz invariants that appear in the original action principle generically. As an application of this formalism, the action principle used by Engle, Pereira, and Rovelli in their spin foam model for gravity is recovered and the coupling of the cosmological constant in such a formulation is obtained.

Key words: BF theory; BF gravity; Immirzi parameter; Holst action.

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