The Quantum Scalar Field in Spherically Symmetric Loop Quantum Gravity
We consider the quantization of a spherically symmetric gravitational system coupled to a massless scalar field within the loop quantum gravity framework. Our results rely on the uniform discretizations method developed during the last years. We minimize the associated discrete “master constraint” using a trial state whose gravitational part is peaked around the classical Schwarzschild solution.
U(N) invariant dynamics for a simplified loop quantum gravity model
The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the recently introduced U(N) framework in order to construct SU(2) invariant operators and define a global U(N) symmetry that will select the homogeneous/isotropic states. Finally, we propose a Hamiltonian operator invariant under area-preserving deformations of the boundary surface and we identify possible connections of this model with Loop Quantum Cosmology.
Revisiting the quantum scalar field in spherically symmetric quantum gravity
We extend previous results in spherically symmetric gravitational systems coupled with a massless scalar field within the loop quantum gravity framework. As starting point, we take the Schwarzschild spacetime. The results presented here rely on the uniform discretization method. We are able to minimize the associated discrete master constraint using a variational method. The trial state for the vacuum consists of a direct product of a Fock vacuum for the matter part and a Gaussian centered around the classical Schwarzschild solution. This paper follows the line of research presented by Gambini, Pullin and Rastgoo and a comparison between their result and the one given in this work is made.
Dynamics for a simple graph using the U(N) framework for loop quantum gravity
The implementation of the dynamics in loop quantum gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We find an interesting global U(N) symmetry in this model that selects the homogeneous/isotropic sector. Then, we propose a quantum Hamiltonian operator for this reduced sector. Finally, we introduce the spinor representation for LQG in order to propose a classical effective dynamics for this model.
Dynamics for a 2-vertex Quantum Gravity Model
We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global …
U(N) tools for loop quantum gravity: the return of the spinor
We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity (LQG) and describe the corresponding phase space in terms of spinors with appropriate constraints. We show how its quantization leads back to the standard Hilbert space of intertwiner states defined as holomorphic functionals. We then explain how to glue these intertwiners states in order to construct spin network states as wave-functions on the spinor phase space. In particular, we translate the usual loop gravity holonomy observables to our classical framework. Finally, we propose how to derive our phase space structure from an action principle which induces non-trivial dynamics for the…