Related papers: Quantum Geometry II : The Mathematics of Loop Quan…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
Quantum gravity has long been thought to be completely decoupled from experiments or observations. Although it is true that smoking guns are still missing, there are now serious hopes that quantum gravity phenomena might be tested. We…
The problem of reconciling general relativity and quantum theory has fascinated and bedeviled physicists for more than 70 years. Despite recent progress in string theory and loop quantum gravity, a complete solution remains out of reach. I…
We look at the various aspects of treating general relativity as a quantum theory. It is briefly studied how to consistently quantize general relativity as an effective field theory. A key achievement here is the long-range low-energy…
Quantum-gravity renders the space-time dimension to depend on the size of region; it monotonically increases with the size of region and asymptotically approaches four for large distances. This effect was discovered in numerical simulations…
Quantizing the gravitational field described by General relativity being a notorious difficult, unsolved and maybe meaningless problem I use in this essay a different strategy: I consider a linear theory in the framework of Special…
We define a three-dimensional quantum theory of gravity as the holographic dual of the Liouville conformal field theory. The theory is consistent and unitary by definition. The corresponding theory of gravity with negative cosmological…
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural…
We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the off-shell (`strong') closure of the constraint algebra is a…
Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the…
General relativity in three spacetime dimensions is used to explore three approaches to the ``problem of time'' in quantum gravity: the internal Schr\"odinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
This note is to bring to the reader's attention the fact that general relativity and quantum mechanics differ from each other in one main aspect. General relativity is based on the diffeomorphism covariant formulation of the laws of physics…
The appearance of infinity together with collapsing quantum state due to the observation or interaction, which are two challenging features of quantum field theory, become very serious problems in quantum gravity as well as in quantum…
Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a…
This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical…
In order to study 3d loop quantum gravity coupled to matter, we consider a simplified model of abelian quantum gravity, the so-called U(1)^3 model. Abelian gravity coupled to a scalar field shares a lot of commonalities with parameterized…
The Immirzi parameter of loop quantum gravity is a one parameter ambiguity of the theory whose precise interpretation is not universally agreed upon. It is an inherent characteristic of the quantum theory as it appears in the spectra of…