Related papers: Three Dimensional Loop Quantum Gravity: Particles …
$SU(\infty)-QGR$ is a foundationally quantum approach to cosmology and gravity. It assumes that the Hilbert space of the Universe as a whole represents the symmetry group $SU(\infty)$, and demonstrates this symmetry for Hilbert spaces of…
We study the quantum geometry of the fuzzy sphere defined as the angular momentum algebra $[x_i,x_j]=2\imath\lambda_p \epsilon_{ijk}x_k$ modulo setting $\sum_i x_i^2$ to a constant, using a recently introduced 3D rotationally invariant…
We present a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. Given any fixed background state representing a non-compact spatial geometry, we use the Gel'fand-Naimark-Segal…
In this work we discuss the holographic description of states in the Hilbert space of (2+1)-dimensional quantum gravity, living on a time slice in the bulk. We focus on pure gravity coupled to pointlike sources for heavy spinning particles.…
We revisit the loop gravity space phase for 3D Riemannian gravity by algebraically constructing the phase space $T^*\mathrm{SU}(2)\sim\mathrm{ISO}(3)$ as the Heisenberg double of the Lie group $\mathrm{SO}(3)$ provided with the trivial…
Loop Quantum Gravity (LQG) is one of the leading approaches to unify quantum physics and General Relativity (GR). The Hilbert space of LQG is spanned by spin-networks which describe the local geometry of quantum space-time. Simulation of…
We highlight the structure and properties of an abstract approach to quantum cosmology and gravity, dubbed $SU(\infty)$-QGR. Beginning from the concept of the Universe as an isolated quantum system, the main axiom of is the existence of an…
It is shown that in two-state quantum theory, a generic quantum state can be described by a non-computable real number. In terms of this, the criterion for measurement outcome is simply and deterministically defined. This demonstration is…
We review quantum gravity model building using the new formalism of `quantum Riemannian geometry' to construct this on finite discrete spaces and on fuzzy ones such as matrix algebras. The formalism starts with a `differential structure' as…
We focus on three-dimensional QRLG with the purpose of shedding light on the link between reduced LQG and LQC in four space-time dimensions. Considering homogeneous three-dimensional LQG, the theory simplifies to QRLG. We then implement…
In loop quantum gravity in the connection representation, the quantum configuration space $\bar{\mathcal{A}/\mathcal{G}}$, which is a compact space, is much larger than the classical configuration space $\mathcal{A}/% \mathcal{G}$ of…
So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the…
We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a…
In loop quantum cosmology the quantum dynamics is well understood. We approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen…
This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and a…
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…
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of…
The loop quantization of 3d gravity consists in defining the Hilbert space of states satisfying the Gau{\ss} constraint and the flatness constraint. The Gau{\ss} constraint is enforced at the kinematical level by introducing spin networks…
Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use…
The free quantum states of topologically massive electrodynamics and gravity in 2+1 dimensions, are explicitly found. It is shown that in both theories the states are described by infrared-regular polarization tensors containing a…