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.
A spin-foam model is derived from the canonical model of Loop Quantum Gravity coupled to a massless scalar field. We generalized to the full theory the scheme first proposed in the context of Loop Quantum Cosmology by Ashtekar, Campiglia and Henderson, later developed by Henderson, Rovelli, Vidotto and Wilson-Ewing.
We model spacetime foam by a gas of virtual wormholes. For a free scalar field we derive the effective Lagrangian which accounts for the interaction with spacetime foam and contains two additional non-local terms. One term describes the scattering of scalar particles on virtual wormholes and explicitly reproduces the Pauli-Villars regularization procedure. The second term describes the back reaction of particles on the number density of wormholes and introduces a self-interaction between particles.
Any approach to pure quantum gravity must eventually face the question of coupling quantum matter to the theory. In the past, several ways of coupling matter to spin foam quantum gravity have been proposed, but the dynamics of the coupled matter-gravity system is challenging to explore. To take first steps towards uncovering the influence quantum matter has on spin foam models, we couple free, massive scalar lattice field theory to a restricted, semi-classical 4d spin foam model, called quantum cuboids. This model can be understood as a superposition of hypercuboidal (and thus irregular) latti…
The influence of spacetime foam on a broad class of bosonic fields with arbitrary numbers of particles in the low energy regime is investigated. Based on recently formulated general description of open quantum gravitational systems, we analyse the propagation of scalar, electromagnetic, and gravitational waves on both long and short time scales with respect to their mean frequencies. For the long time propagation, the Markov approximation is employed that neglects the effects of initial conditions of these waves. In this case, despite intuitively expected decoherence and dissipation from the n…
We construct a group field theory model for quantum gravity minimally coupled to relativistic scalar fields, defining as well a corresponding discrete gravity path integral (and, implicitly, a coupled spin foam model) in its Feynman expansion. We also analyze a number of variations of the same model, the corresponding discrete gravity path integrals, its generalization to the coupling of multiple scalar fields and discuss its possible applications to the extraction of effective cosmological dynamics from the full quantum gravity formalism, in the context of group field theory condensate cosmol…
A finiteness bound for the EPRL/FK spin foam model
证明了当顶点振幅除以顶点自旋维数乘积的适当幂$p$时，量子引力的EPRL/FK自旋泡沫模型具有绝对收敛的配分函数.这个权力是独立的自旋泡沫2-复杂的，我们发现，$p>2$确保状态和的收敛。确定值$0 \le p \le 2$的状态和的收敛性需要知道当一些顶点自旋大而其他顶点自旋小时顶点振幅的大自旋渐近性。
We formulate the spin foam representation of discrete SU(2) gauge theory as a product of vertex amplitudes each of which is the spin network generating function of the boundary graph dual to the vertex. In doing so the sums over spins have been carried out. The boundary data of each n-valent node is explicitly reduced with respect to the local gauge invariance and has a manifest geometrical interpretation as a framed polyhedron of fixed total area. Ultimately, sums over spins are traded for contour integrals over simple poles and recoupling theory is avoided using generating functions.
