Related papers: Loop Representations
Loop quantum gravity is a mature theory. To proceed to explicit calculations in cosmology, it is necessary to make assumptions and simplifications based on the symmetries of the cosmological setting. Symmetry reduction is especially…
Canonical quantization is often used to suggest new effects in quantum gravity, in the dynamics as well as the structure of space-time. Usually, possible phenomena are first seen in a modified version of the classical dynamics, for instance…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
We first motivate the study of a certain quotient of the loop braid category, both for the mathematics underpinning recent approaches to topological quantum computation; and as a key example in non-semisimple higher representation theory.…
Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual…
The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a…
Only the position representation is used in introductory quantum mechanics and the momentum representation is not usually presented until advanced undergraduate courses. To emphasize the relativity of the representations of the abstract…
This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The…
This is a brief and updated summary of a talk given at the International Conference on Gravitation and Cosmology that took place in Poona in December 1995. It is very brief and is mostly intended as a guide to current literature, or to keep…
Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to…
This article describes the regularization of the generally relativistic gauge field representation of gravity on a piecewise linear lattice. It is a part of the program concerning the classical relativistic theory of fundamental…
After a brief introduction, basic ideas of the quantum Riemannian geometry underlying loop quantum gravity are summarized. To illustrate physical ramifications of quantum geometry, the framework is then applied to homogeneous isotropic…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
Loop Quantum Gravity (LQG) is a promising approach to quantum gravity, in particular because it is based on a rigorous quantization of the kinematics of gravity. A difficult and still open problem in the LQG program is the construction of…
Canonical methods allow the derivation of effective gravitational actions from the behavior of space-time deformations reflecting general covariance. With quantum effects, the deformations and correspondingly the effective actions change,…
New and non-trivial properties of off-shell instantons in loop quantum cosmology show that dynamical signature change naturally cures recently observed problems in the semiclassical path integral of quantum gravity. If left unsolved, these…
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…
The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity (LQG) is a promising proposal for…
Recent advances in classical machine learning have shown that creating models with inductive biases encoding the symmetries of a problem can greatly improve performance. Importation of these ideas, combined with an existing rich body of…
Loop quantum gravity introduces strong non-perturbative modifications to the dynamical equations in the semi-classical regime, which are responsible for various novel effects, including resolution of the classical singularity in a Friedman…