BF gravity and the Immirzi parameter

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

doi:10.1088/0264-9381/18/5/101

Cited by 58 publications

(99 citation statements)

References 27 publications

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“…This gives a direct evidence that the Immirzi parameter has no importance in our problem. 3 In [21] the Immirzi parameter was introduced in a different way. The difference comes from the Lagrange multiplier ϕ which was chosen to be a Lie-algebra valued field ϕ IJKL , whereas it is a density tensor ϕ µνρσ in our case.…”

Section: Notes On the Immirzi Parametermentioning

confidence: 99%

Plebanski theory and covariant canonical formulation

Alexandrov¹,

Buffenoir²,

Roché

2007

Class. Quantum Grav.

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We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the HilbertPalatini action. This is done by comparing the symplectic structures of the two theories through the computation of Dirac brackets. We also construct a shifted connection with simplified Dirac brackets, playing an important role in the covariant loop quantization program, in the Plebanski framework. Implications for spin foam models are also discussed.

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Section: Notes On the Immirzi Parametermentioning

confidence: 99%

Plebanski theory and covariant canonical formulation

Alexandrov¹,

Buffenoir²,

Roché

2007

Class. Quantum Grav.

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“…Recently [75] it was also shown that the Barrett-Crane model arises quite naturally from a spin foam quantization of the most general BF-type action for gravity, proposed in [76], in the sense that a discretization of the constraints reducing BF theory to gravity in this new action shows their equivalence with the Barrett-Crane constraints on bivectors, and that a translation of them into conditions on the representations of the Lie algebra also gives the Barrett-Crane quantum constraints. This suggests the uniqueness of the Barrett-Crane constraints, in the sense that they arise whenever we express gravity in terms of 2-forms.…”

Section: Barrett-crane Model Plebanski Action Bf Theory and Generalmentioning

confidence: 99%

Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity

2001

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This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity, topological quantum field theories, path integral quantum gravity, lattice gauge theory, matrix models, category theory, statistical mechanics. We describe the general formalism and ideas of spin foam models, the picture of quantum geometry emerging from them, and give a review of the results obtained so far, in both the Euclidean and Lorentzian case. We focus in particular on the Barrett-Crane model for 4-dimensional quantum gravity.

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“…where the {j i } have integers and half-integers values, l p = (hG/c) 1/2 = 10 −33 cm is the Planck length and γ is a constant analogous to the Immirzi parameter [3]. The spectrum of the area operator is a very important result of loop quantum gravity.…”

mentioning

confidence: 99%

Note about the quantum of area in a noncommutative space

2003

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In this note we show that in a two-dimensional non-commutative space the area operator is quantized, this outcome is compared with the result obtained by Loop Quantum Gravity methods.PACS numbers: 02.40. Gh, 03.65.Bz One of the most relevant results of quantum mechanics is that physical quantities as the energy and the angular momenta, can have a discrete spectra. In fact, this theory begins with the Planck idea about the quantum nature of light. In contrast, general relativity modifies our understanding of gravity not as a force but as geometry. In recent years, there are several attempts to reconcile the ideas of quantum mechanics and general relativity. This implies in principle to change the geometrical properties of the space-time at the Planck length scales [1]. One of this attempt is the loop quantum gravity [2]. A remarkable result of this theory, is that geometrical operators as area or volume have discrete spectra at the Planck length order. For instance, one can define an operator for the area which has the spectrumwhere the {j i } have integers and half-integers values, l p = (hG/c) 1/2 = 10 −33 cm is the Planck length and γ is a constant analogous to the Immirzi 1

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BF gravity and the Immirzi parameter

Cited by 58 publications

References 27 publications

Plebanski theory and covariant canonical formulation

Plebanski theory and covariant canonical formulation

Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity

Note about the quantum of area in a noncommutative space

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