Papers by Roberto Pereira
Classical and Quantum Gravity, 2010
The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graph... more The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics.
We generalize a model recently proposed for Euclidean quantum gravity to the case of Lorentzian s... more We generalize a model recently proposed for Euclidean quantum gravity to the case of Lorentzian signature. The main features of the Euclidean model are preserved in the Lorentzian one. In particular, the boundary Hilbert space matches the one of SU(2) loop quantum gravity. As in the Euclidean case, the model can be obtained from the Lorentzian Barrett-Crane model from a flipping of the Poisson structure, or alternatively, by adding a topological term to the action and taking the small Barbero-Immirzi parameter limit.
Nuclear Physics B, 2008
We introduce a vertex amplitude for 4d loop quantum gravity. We derive it from a conventional qua... more We introduce a vertex amplitude for 4d loop quantum gravity. We derive it from a conventional quantization of a Regge discretization of euclidean general relativity. This yields a spinfoam sum that corrects some difficulties of the Barrett-Crane theory. The second class simplicity constraints are imposed weakly, and not strongly as in Barrett-Crane theory. Thanks to a flip in the quantum algebra, the boundary states turn out to match those of SO(3) loop quantum gravity -the two can be identified as eigenstates of the same physical quantities -providing a solution to the problem of connecting the covariant SO(4) spinfoam formalism with the canonical SO(3) spin-network one. The vertex amplitude is SO(3) and SO(4)-covariant. It rectifies the triviality of the intertwiner dependence of the Barrett-Crane vertex, which is responsible for its failure to yield the correct propagator tensorial structure. The construction provides also an independent derivation of the kinematics of loop quantum gravity and of the result that geometry is quantized. (Aix-Marseille II) et du Sud (Toulon-Var); laboratoire affiliéà la FRUMAM (FR 2291).
Physical Review Letters, 2007
Spinfoam theories are hoped to provide the dynamics of non-perturbative loop quantum gravity. But... more Spinfoam theories are hoped to provide the dynamics of non-perturbative loop quantum gravity. But a number of their features remain elusive. The best studied one -the euclidean Barrett-Crane model- does not have the boundary state space needed for this, and there are recent indications that, consequently, it may fail to yield the correct low-energy $n$-point functions. These difficulties can be traced to the SO(4) -> SU(2) gauge fixing and the way certain second class constraints are imposed, arguably incorrectly, strongly. We present an alternative model, that can be derived as a bona fide quantization of a Regge discretization of euclidean general relativity, and where the constraints are imposed weakly. Its state space is a natural subspace of the SO(4) spin-network space and matches the SO(3) hamiltonian spin network space. The model provides a long sought SO(4)-covariant vertex amplitude for loop quantum gravity.
Nuclear Physics B, 2008
We extend the definition of the "flipped" loop-quantum-gravity vertex to the case of a finite Imm... more We extend the definition of the "flipped" loop-quantum-gravity vertex to the case of a finite Immirzi parameter γ. We cover both the euclidean and lorentzian cases. We show that the resulting dynamics is defined on a Hilbert space isomorphic to the one of loop quantum gravity, and that the area operator has the same discrete spectrum as in loop quantum gravity. This includes the correct dependence on γ, and, remarkably, holds in the lorentzian case as well. The ad hoc flip of the symplectic structure that was required to derive the flipped vertex is not anymore required for finite γ. These results establish a bridge between canonical loop quantum gravity and the spinfoam formalism in four dimensions.
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Papers by Roberto Pereira