Related papers: Polyhedra in loop quantum gravity

In this paper, we carry out the entanglement calculations on the coherent intertwiners. We first consider the entanglement introduced by the group-averaging of the tensor-product type intertwiner on a four-valents vertex. The result shows…

We summarize recent developments at the interface of quantum gravity and quantum information, and discuss applications to the quantum geometry of space in loop quantum gravity. In particular, we describe the notions of link entanglement,…

We consider convex spacelike polyhedra oriented in Minkowski space. These are the classical analogues of spinfoam intertwiners. We point out a parametrization of these shapes using null face normals, with no constraints or redundancies. Our…

In this paper, we develop a quantum theory of homogeneously curved tetrahedron geometry, by applying the combinatorial quantization to the phase space of tetrahedron shapes defined in arXiv:1506.03053. Our method is based on the relation…

The space $\mathrm{Inv}(j_1,j_2,j_3,j_4)$ of SU(2)-invariant four-valent tensors, also known as intertwiners, can be understood as the quantum states of a tetrahedron in Euclidean space with fixed areas. In loop quantum gravity, they are…

Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum…

In this paper, we construct the phase space of a constantly curved tetrahedron with fixed triangle areas in terms of a pair of Darboux coordinates called the length and twist coordinates, which are in analogy to the Fenchel-Nielsen…

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…

In the context of loop quantum gravity and spinfoam models, the simplicity constraints are essential in that they allow to write general relativity as a constrained topological BF theory. In this work, we apply the recently developed U(N)…

In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum…

In the context of quantum gravity, we clarify entanglement calculations on spin networks: we distinguish the gauge-invariant entanglement between intertwiners located at the nodes and the entanglement between spin states located on the…

A new link between tetrahedra and the group SU(2) is pointed out: by associating to each face of a tetrahedron an irreducible unitary SU(2) representation and by imposing that the faces close, the concept of quantum tetrahedron is seen to…

We propose a new treatment of the quantum simplicity constraints appearing in the general ${SO(D+1)}$ formulation of loop quantum gravity for the ${(1+D)}$-dimensional space-time. Instead of strongly imposing the constraints, we construct a…

We introduce a new technique for dealing with the matrix elements of the Hamiltonian operator in loop quantum gravity, based on the use of intertwiners projected on coherent states of angular momentum. We give explicit expressions for the…

We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in…

We introduce the set of framed convex polyhedra with N faces as the symplectic quotient C^2N//SU(2). A framed polyhedron is then parametrized by N spinors living in C^2 satisfying suitable closure constraints and defines a usual convex…

The closure constraint is a central piece of the mathematics of loop quantum gravity. It encodes the gauge invariance of the spin network states of quantum geometry and provides them with a geometrical interpretation: each decorated vertex…

We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to…

In this work we study the Hilbert space space of N-valent SU(2) intertwiners with fixed total spin, which can be identified, at the classical level, with a space of convex polyhedra with N face and fixed total boundary area. We show that…

We investigate the entropy counting for black hole horizons in loop quantum gravity (LQG). We argue that the space of 3d closed polyhedra is the classical counterpart of the space of SU(2) intertwiners at the quantum level. Then computing…