arXiv subjects
Publications and source records attributed to Emanuele Alesci.
We continue the semiclassical analysis, started in a previous paper, of the intertwiner sector of the flipped vertex spinfoam model. We use independently both a semi-analytical and a purely numerical approach, finding the correct behavior of wave packet propagation and physical expectation values. In the end, we show preliminary results about correlation functions.
This paper aims at clarifying the link between Loop Quantum Gravity and Spin-Foam models in four dimensions. Starting from the canonical framework, we construct an operator P acting on the space of cylindrical functions Cyl($Γ$), where $Γ$ is the 4-simplex graph, such that its ma- trix elements are, up to some normalization factors, the vertex amplitude of Spin-Foam models. The Spin-Foam models we are considering are the topological model, the Barrett-Crane model and the Engle-Pereira-Rovelli model. The operator P is usually called the "projector" into physical states and its matrix elements gives the physical scalar product. Therefore, we relate the physical scalar product of Loop Quantum Gravity to vertex amplitudes of some Spin-Foam models. We discuss the possibility to extend the action of P to any cylindrical functions on the space manifold.
We review the construction of the tensorial structure of the graviton propagator in the context of loop quantum gravity and spinfoam formalism. The main result of this analysis is that applying the same strategy used to compute the diagonal terms, the Barrett-Crane vertex is unable to yield the correct propagator in the long distance limit. The problem is in the intertwiner-independence of the Barrett-Crane vertex. We also review the asymptotic behavior of an alternative vertex that is able to give the correct propagator.
In a previous article we have show that there are difficulties in obtaining the correct graviton propagator from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude that depends nontrivially on the intertwiners can yield the correct propagator. We give an explicit example of asymptotic behavior of a vertex amplitude that gives the correct full graviton propagator in the large distance limit.
Some components of the graviton two-point function have been recently computed in the context of loop quantum gravity, using the spinfoam Barrett-Crane vertex. We complete the calculation of the remaining components. We find that, under our assumptions, the Barrett-Crane vertex does not yield the correct long distance limit. We argue that the problem is general and can be traced to the intertwiner-independence of the Barrett-Crane vertex, and therefore to the well-known mismatch between the Barrett-Crane formalism and the standard canonical spin networks. In a companion paper we illustrate the asymptotic behavior of a vertex amplitude that can correct this difficulty.
The main issue of the present letter is to fix specific features (which turn out being independent of extradimension size) of gravitational waves generated before a dimensional compactification process. Valuable is the possibility to detect our prediction from gravitational wave experiment without high energy laboratory investigation. In particular we show how gravitational waves can bring information on the number of Universe dimensions. Within the framework of Kaluza-Klein hypotheses, a different morphology arises between waves generated before than the compactification process settled down and ordinary 4-dimensional waves. In the former case the scalar and tensor degrees of freedom can not be resolved. As a consequence if were detected gravitational waves having the feature here predicted (anomalous polarization amplitudes), then they would be reliable markers for the existence of an extra dimension.
In the present work we analize the behavior of 5-dimensional gravitational waves propagating on a Kaluza-Klein background and we face separately the two cases in which respectively the waves are generated before and after the process of dimensional compactification. We show that if the waves are originated on a 5-d space-time which fulfills the principle of general relativity, then the process of compactification can not reduce the dynamics to the pure 4-dimensional scalar, vector and tensor degrees of freedom. In particular, while the electromagnetic waves evolve independently, the scalar and tensor fields couple to each other; this feature appears because, when the gauge conditions are splitted, the presence of the scalar ripple prevents that the 4-d gravitational waves are traceless. The phenomenological issue of this scheme consists of an anomalous relative amplitude of the two independent polarizations which characterize the 4-d gravitational waves. Such profile of polarization amplitudes, if detected, would outline the extra-dimension in a very reliable way, because a wave with non-zero trace can not arise from ordinary matter sources. We discuss the above mentioned phenomenon either in the case of a unit constant value of the background scalar component (when the geodesic deviation is treated with precise outputs), and assuming such background field as a dynamical degree (only qualitative conclusion are provided here, because the details of the polarization amplitudes depend on the choice of specific metric forms). Finally we perturb a real Kaluza-Klein theory showing that in this context, while the electromagnetic waves propagate independently, the 4-d gravitational waves preserve their ordinary structure, while the scalar plays for them the role of source.