Related papers: Symmetric States in Quantum Geometry
Counting of microscopic states of black holes is discussed within the framework of loop quantum gravity. There are two different ways, one allowing for all spin states and the other involving only pure horizon states. The number of states…
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically symmetric quantum geometry, as well as…
A state of a black hole in loop quantum gravity is given by a distribution of spins on punctures on the horizon. The distribution is of the Boltzmann type, with the area playing the role of the energy. In investigations where the total area…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
It is a tantalising possibility that quantum gravity (QG) states remaining coherent at astrophysical, galactic and cosmological scales could exist and that they could play a crucial role in understanding macroscopic gravitational effects.…
In the realm of a quantum cosmological model for dark energy in which we have been able to construct a well-defined Hilbert space, a consistent coherent state representation has been formulated that may describe the quantum state of the…
The holographic state of matter exists in the quantum gravitational regime, with black holes as the example. In this essay, we provide a microscopic derivation to the holographic thermodynamics and further discuss its implications for…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
We adopt the point of view that (Riemannian) classical and (loop-based) quantum descriptions of geometry are macro- and micro-descriptions in the usual statistical mechanical sense. This gives rise to the notion of geometrical entropy,…
We introduce a class of states characterized by proposed conditions of homogeneity and isotropy in loop quantum gravity and construct concrete examples given by Bell-network states on a special class of homogeneous graphs. Such states…
In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity. First, we introduce a rigorous formulation of an embedding proposed by Bojowald and Kastrup, of LQC states into loop…
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
We continue our investigation of an improved quantization scheme for spherically symmetric loop quantum gravity. We find that in the region where the black hole singularity appears in the classical theory, the quantum theory contains…
The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…
In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of…
The quantum theory of the spherically symmetric gravity in 3+1 dimensions is investigated. The functional measures are explicitly evaluated and the physical state conditions are derived by using the technique developed in two dimensional…