Related papers: Angular Momentum in Loop Quantum Gravity
We investigate how a uniformly rotating frame is defined as the rest frame of an observer rotating with constant angular velocity $\Omega$ around the $z$ axis of an inertial frame. Assuming that this frame is a Lorentz one, we second…
An outstanding open issue in our quest for physics beyond Einstein is the unification of general relativity (GR) and quantum physics. Loop quantum gravity (LQG) is a leading approach toward this goal. At its heart is the central lesson of…
The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the Hamiltonian operator, and of…
We construct the operator that projects on the physical states in loop quantum gravity. To this aim, we consider a diffeomorphism invariant functional integral over scalar functions. The construction defines a covariant, Feynman-like,…
Momentum is analyzed as a random variable in stochastic quantum mechanics. Arbitrary potential energy functions are considered. The oscillator is presented as an example.
Symmetric states are defined in the kinematical sector of loop quantum gravity and applied to spherical symmetry and homogeneity. Consequences for the physics of black holes and cosmology are discussed.
It is congruous with the quantum nature of the world to view the space-time geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the space-time manifold as a purely…
Angular momentum can be defined by rearranging the Komar surface integral in terms of a twist form, encoding the twisting around of space-time due to a rotating mass, and an axial vector. If the axial vector is a coordinate vector and has…
In loop quantum gravity, the area element of embedded spatial surfaces is given by a well-defined operator. We further characterize the quantized geometry of such surfaces by proposing definitions for operators quantizing scalar curvature…
We give an account of the state of the art about black hole entropy in Loop Quantum Gravity. This chapter contains a historical summary and explains how black hole entropy is described by relying on the concept of isolated horizon, with an…
Loop Quantum Gravity is now a well established approach to quantum gravity. One of the main challenges still faced by the theory is constructing a consistent dynamics which would lead back to the standard dynamics of the gravitational field…
We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.
I summarize the basic ideas and formalism of loop quantum gravity. I illustrate the results on the discrete aspects of quantum geometry and two applications of these results to black hole physics. In particular, I discuss in detail a…
We propose an algebra of operators along an observer's worldline as a background-independent algebra in quantum gravity. In that context, it is natural to think of the Hartle-Hawking no boundary state as a universal state of maximum…
We study perturbative noncommutative quantum gravity by expanding the gravitational field about a fixed classical background. A calculation of the one loop gravitational self-energy graph reveals that only the non-planar graviton loops are…
In this note we show that in a two-dimensional non-commutative space the area operator is quantized, this outcome is compared with the result obtained by Loop Quantum Gravity methods.
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
Using the method of canonical group quantization, we construct the angular momentum operators associated to configuration spaces with the topology of (i) a sphere and (ii) a projective plane. In the first case, the obtained angular momentum…
This note aims to offer a non-technical and self-contained introduction to gravitational algebras and their applications in the nonequilibrium physics of gravitational systems. We begin by presenting foundational concepts from operator…
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area…