Cartan’s equations define a topological field theory of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mi>F</mml:mi></mml:math>type

Cuesta, Vladimir; Montesinos, Merced

doi:10.1103/physrevd.76.104004

Cited by 22 publications

(55 citation statements)

References 20 publications

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“…The main assumption made about the frame field is that it is non-degenerate, and the matrix e A a is invertible. In the form of the action we may recognize the special case of the theory [43,44], designed to obey the Cartan's (also Bianchi's) structure equations (which are the kinematical basis for Riemannian geometry). One could anticipate and announce (4.4) as the Poincaré BF theory -this assertion is made precise, as we develop in this section the structure of the theory in full detail.…”

Section: The Extended Bf Action With the Frame Fieldmentioning

confidence: 99%

Poincaré–Plebański formulation of GR and dual simplicity constraints

Belov

2018

Class. Quantum Grav.

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We revise the classical continuum formulation behind the Spin Foam approach to the quantization of gravity. Based on the recent applications of the current EPRL-FK model beyond triangulations, we identify the tension with the implementation of the 'volume' part of simplicity constraints, required for the passage from the topological BF theory to gravity. The crucial role, played by 4d normals in the linear version of constraints, necessitates the extension of the configuration space, and we argue to switch from normal 3-forms directly to tetrads. The requirement of vanishing torsion leads to consider first an unconstrained extended Poincaré BF theory, which we characterize fully both at the Lagrangian and Hamiltonian levels, paying special attention to its gauge symmetries. The simplicity constraints are introduced naturally, in the spirit of Plebański formulation, and we give their tetradic version, dual to that of using 3-forms. This brings us much closer to the geometric content of General Relativity.

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Section: The Extended Bf Action With the Frame Fieldmentioning

confidence: 99%

Poincaré–Plebański formulation of GR and dual simplicity constraints

Belov

2018

Class. Quantum Grav.

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“…Observe also that different combinations of those terms allow us to make the coupling of the Yang-Mills field into the action principle (1). (ii) Notice that a term of the form 3 2 a IJ b KL Ã B IJ^Ã B KL can be added to the action principle (33). If such a term is included its effect would be a redefinition of the 1 parameter.…”

Section: B Case B Ij ¼ 2 E I^ejmentioning

confidence: 99%

“…Just to mention some of them, Cartan's equations in the framework of BF theories are analyzed in Refs. [3,4] while the relationship of general relativity to the Husain-Kuchar model in the framework of BF theory is analyzed in Refs. [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

BF gravity with Immirzi parameter and matter fields

Montesinos¹,

Velázquez²

2012

Phys. Rev. D

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We perform the coupling of the scalar, Maxwell, and Yang-Mills fields as well as the cosmological constant to BF gravity with Immirzi parameter. The proposed action principles employ auxiliary fields in order to keep a polynomial dependence on the B fields. By handling the equations of motion for the B field and for the auxiliary fields, these latter can be expressed in terms of the physical fields and by substituting these expressions into the original action principles we recover the first-order (Holst) and second-order actions for gravity coupled to the physical matter fields. We consider these results a relevant step towards the understanding of the coupling of matter fields to gravity in the theoretical framework of BF theory.Comment: To appear in Phys. Rev D, 9 pages, LaTeX fil

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“…In [20] was proposed to consider the action S 2 [e, A] as a genuine field theory in its own right because it is background-independent and diffeomorphism-invariant. Recently, it has been shown that S 2 [e, A] is indeed topological if the spacetime M 4 has no boundary.…”

Section: Cmpr Action For Gravitymentioning

confidence: 99%

Equivalent and Alternative Forms for BF Gravity with Immirzi Parameter

Montesinos

Velázquez

2011

SIGMA

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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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Cartan’s equations define a topological field theory of theBFtype

Cited by 22 publications

References 20 publications

Poincaré–Plebański formulation of GR and dual simplicity constraints

Poincaré–Plebański formulation of GR and dual simplicity constraints

BF gravity with Immirzi parameter and matter fields

Equivalent and Alternative Forms for BF Gravity with Immirzi Parameter

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