Equivalent and Alternative Forms for BF Gravity with Immirzi Parameter

Abstract

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.

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• Flipped spinfoam vertex and loop gravity
• Lorentz covariance of loop quantum gravity
• The new vertices and canonical quantization
• Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories
• BF gravity with Immirzi parameter and cosmological constant
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Cited by in corpus (6)

• The Spin Foam Approach to Quantum Gravity
• $BF$ gravity
• BF gravity with Immirzi parameter and matter fields
• Barbero's formulation from a $BF$-type action with the Immirzi parameter
• Polysymplectic formulation for BF gravity with Immirzi parameter
• Canonical analysis with no second-class constraints of $BF$ gravity with Immirzi parameter