BF gravity and the Immirzi parameter

Capovilla, Riccardo; Montesinos, Merced; Prieto, Violeta; Rojas, Efraín

doi:10.1088/0264-9381/18/6/501

Cited by 29 publications

(52 citation statements)

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“…The first BF principle to describe pure gravity including the Immirzi parameter was introduced in Ref. [12] and is given by…”

Section: Hamiltonian Analysis Of the Cmpr Actionmentioning

confidence: 99%

“…Afterwards, Holst introduced a modification of the Hilbert-Palatini action and it was showed that Barbero's formulation was the Hamiltonian form of this action principle [8,9]. Moreover, real general relativity was also written as a constrained BF theory [10,11] and later works generalized the constraint on the B field [12,13] in such a way that by solving it the Immirzi parameter γ [14], a free parameter appearing in Barbero's formulation, was naturally included.…”

Section: Introductionmentioning

confidence: 99%

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Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter

Celada

Montesinos

2012

Class. Quantum Grav.

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We perform the Lorentz-covariant Hamiltonian analysis of two Lagrangian action principles that describe general relativity as a constrained BF theory and that include the Immirzi parameter. The relation between these two Lagrangian actions has been already studied through a map among the fields involved. The main difference between these is the way the Immirzi parameter is included, since in one of them the Immirzi parameter is included explicitly in the BF terms, whereas in the other (the CMPR action) it is in the constraint on the B fields. In this work we continue the analysis of their relationship but at the Hamiltonian level. Particularly, we are interested in seeing how the above difference appears in the constraint structure of both action principles. We find that they both possess the same number of firstclass and second-class constraints and satisfy a very similar (off-shell) Poisson-bracket algebra on account of the type of canonical variables employed. The two algebras can be transformed into each other by making a suitable change of variables.

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“…The first BF principle to describe pure gravity including the Immirzi parameter was introduced in Ref. [12] and is given by…”

Section: Hamiltonian Analysis Of the Cmpr Actionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter

Celada

Montesinos

2012

Class. Quantum Grav.

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“…One way to overcome the problem is to modify the Plebanski theory such that it does not admit the topological solutions anymore. There is a way to do so [20] but the price to pay is that classical solutions are those of gravity with an Immirzi parameter γ supplemented with those of gravity with the inverse parameter γ −1 . Thus, the path integral can be performed and can be shown, as expected, to mix both types of solutions.…”

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confidence: 99%

Cosmological Plebanski theory

Noui

Pérez²,

Vandersloot

2009

Gen Relativ Gravit

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We consider the cosmological symmetry reduction of the Plebanski action as a toy-model to explore, in this simple framework, some issues related to loop quantum gravity and spin-foam models. We make the classical analysis of the model and perform both path integral and canonical quantizations. As for the full theory, the reduced model admits two types of classical solutions: topological and gravitational ones. The quantization mixes these two solutions, which prevents the model to be equivalent to standard quantum cosmology. Furthermore, the topological solution dominates at the classical limit. We also study the effect of an Immirzi parameter in the model.Comment: 20 page

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“…al. (CMPR action) [9] but before we integrate out the metric variable in this action, we will give some details over the Cartan-Killing form and the auxiliary fields, so that we'll obtain an adequate pure connection formulation from where maximally symmetric spaces will appear as solutions from its variational principles. The organization of the paper is as follows.…”

Section: Introductionmentioning

confidence: 99%

“…At the middle of the seventies of the last century, Plebański considered self-dual quantities by a complexified SO(3) group, but in order to describe Lorentzian signature spacetime it was necessary to impose certain reality conditions [11]. Here, we consider one of the most well-known BF action functional which give rise to an action for GR with Immirzi parameter [9], by considering SO(1, 3) as our internal symmetry group…”

Section: Introductionmentioning

confidence: 99%

A pure connection formulation with real fields for Gravity

Rosales-Quintero

2020

Preprint

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We study an SO(1, 3) pure connection formulation in four dimensions for real-valued fields, inspired by the Capovilla, Dell and Jacobson complex self-dual approach. By considering the CMPR BF action, also, taking into account a more general class of the Cartan-Killing form for the Lie algebra so(1, 3) and by refining the structure of the Lagrange multipliers, we integrate out the metric variables in order to obtain the pure connection action. Once we have obtained this action, we impose certain restrictions on the Lagrange multipliers, in such a way that the equations of motion led us to a family of torsionless conformally flat Einstein manifolds, parametrized by two numbers. Finally, we show that, by a suitable choice of parameters, that self-dual spaces (Anti-) De Sitter can be obtained.

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BF gravity and the Immirzi parameter

Abstract: The publishers would like to apologize for an error occurring in issue 5 (7 March 2001) of Classical and Quantum Gravity. The article by Capovilla et al was published as a Letter to the Editor, when it should have appeared as a Paper.

Cited by 29 publications

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Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter

Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter

Cosmological Plebanski theory

A pure connection formulation with real fields for Gravity

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