Ref HAL: hal-00326626_v1
Exporter : BibTex | endNote
Résumé:

After a brief sketch of covariant loop quantization I'll demonstrate that the consistent implementation of second class constraints in the discretized path integral for 4d general relativity leads to a spin foam model with boundary states identical to the kinematical states of the loop approach. The identification works perfectly well for any signature and any value of the Immirzi parameter. An expression for the vertex amplitude is given in terms of integrated (over a still unknown measure) projected spin networks.

Ref HAL: hal-00326622_v1
Exporter : BibTex | endNote
Résumé:

After a brief review of a covariant approach to loop quantum gravity and of important notion of projected spin networks, I revise the spin foam quantization procedure of 4-dimensional general relativity. In particular, I discuss how the simplicity and the closure constraints should be implemented and demonstrate the precise agreement between the canonical and the path integral quantizations at the kinematical level.

Ref HAL: hal-00325481_v1
Ref Arxiv: 0809.4763
DOI: 10.1088/0264-9381/26/5/055005
WoS: 000263493200006
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
33 Citations
Résumé:

We consider non-chiral, full Lorentz group-based Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Phi with ``internal'' indices. The Hamiltonian analysis of this version of the theory turns out to be simpler than in the previously considered in the literature version with Phi carrying spacetime indices. We then extend the Hamiltonian analysis to a more general class of theories whose action contains scalars invariants constructed from Phi. Such theories have recently been considered in the context of unification of gravity with other forces. We show that these more general theories have six additional propagating degrees of freedom as compared to general relativity, something that has not been appreciated in the literature treating them as being not much different from GR.

Ref HAL: hal-00292412_v1
Ref Arxiv: 0806.4620
DOI: 10.1007/s11005-009-0305-8
WoS: 000263918200003
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
26 Citations
Résumé:

We study general linear perturbations of a class of 4d real-dimensional hyperkahler manifolds obtainable by the (generalized) Legendre transform method. Using twistor methods, we show that deformations can be encoded in a set of holomorphic functions of 2d+1 variables, as opposed to the functions of d+1 variables controlling the unperturbed metric. Such deformations generically break all tri-holomorphic isometries of the unperturbed metric. Geometrically, these functions generate the symplectomorphisms which relate local complex Darboux coordinate systems in different patches of the twistor space. The deformed Kahler potential follows from these data by a Penrose-type transform. As an illustration of our general framework, we determine the leading exponential deviation of the Atiyah-Hitchin manifold away from its negative mass Taub-NUT limit. In a companion paper, we extend these techniques to quaternionic-Kahler spaces with isometries.

Commentaires: 44 pages, 2 figures, uses JHEP3.cls

Ref HAL: hal-00264038_v1
Ref Arxiv: 0802.3389
DOI: 10.1103/PhysRevD.78.044033
WoS: 000259368500081
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
35 Citations
Résumé:

We revise imposition of various constraints in spin foam models of 4-dimensional general relativity. We argue that the usual simplicity constraint must be supplemented by a constraint on holonomies and together they must be inserted explicitly into the discretized path integral. At the same time, the closure constraint must be relaxed so that the new constraint expresses covariance of intertwiners assigned to tetrahedra by spin foam quantization. As a result, the spin foam boundary states are shown to be realized in terms of projected spin networks of the covariant loop approach to quantum gravity.

Ref HAL: hal-00264039_v1
Ref Arxiv: 0802.1221
DOI: 10.1088/0264-9381/25/14/145012
WoS: 000257326100014
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
42 Citations
Résumé:

We clarify the role played by the Immirzi parameter in classical gravity coupled to fermions. Considering the general non-minimal coupling, we show that, although the torsion depends explicitly on the Immirzi parameter, in a suitable parametrization the effective action obtained by integrating out the spin-connection is independent of it. Thus the Immirzi parameter is not detectable in classical theory even after coupling of fermions.

Ref HAL: in2p3-00152760_v1
Ref Arxiv: 0705.3892
DOI: 10.1103/PhysRevD.77.024009
WoS: 000252864000059
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
31 Citations
Résumé:

We suggest a modification of the Barrett-Crane spin foam model of 4-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found as a space of the so-called projected spin networks. These spin networks are identified with the boundary states of a spin foam model and provide a generalization of the unique Barrette-Crane intertwiner. We propose a way to modify the Barrett-Crane quantization procedure to arrive at this generalization: the $B$ field (bi-vectors) should be promoted not to generators of the gauge algebra, but to their certain projection. The modification is also justified by the canonical analysis of Plebanski formulation. Finally, we compare our construction with other proposals to modify the Barret-Crane model.

Commentaires: 15 pages