Related papers: Quantum Geometry I : Basics of Loop Quantum Gravit…
It is shown that the recently geometric formulation of quantum mechanics implies the use of Weyl geometry. It is discussed that the natural framework for both gravity and quantum is Weyl geometry. At the end a Weyl invariant theory is…
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
Differential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantum gauge theory of gravity which is proposed in the references hep-th/0109145 and hep-th/0112062 is formulated completely in the…
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime…
Black Holes have always played a central role in investigations of quantum gravity. This includes both conceptual issues such as the role of classical singularities and information loss, and technical ones to probe the consistency of…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
Each approach to the quantum-gravity problem originates from expertise in one or another area of theoretical physics. The particle-physics perspective encourages one to attempt to reproduce in quantum gravity as much as possible of the…
Over the last three years, a number of fundamental issues in quantum gravity were addressed in the framework of quantum geometry, discussed extensively by John Baez in this conference. In particular, these include: A statistical mechanical…
General covariance in quantum gravity is seen once one integrates over all possible metrics. In recent years topological field theories have given us a different route to general covariance without integrating over all possible metrics.…
This introductory review is addressed to beginning researchers. Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models. In particular, these examples illustrate: i) how…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
The general problems of three-dimensional quantum gravity are recatitulated here, putting the emphasis on the mathematical problems of defining the measure of the path integral over all three-dimensional metrics.This work should be viewed…
I have shown that the field defined by the Wheeler-DeWitt equation for \textit{pure gravity} is neither a standard gravitational field nor the field representing a particular universe. The theory offers a unified description of geometry and…
The paper concerns the fictitious entanglement of the so-called ``singularities'' in problems, pertaining to quantum gravity, due, in point of fact, to the way we try to employ, in that context, differential geometry, the latter being…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…
In recent years, Loop Quantum Gravity has emerged as a solid candidate for a nonperturbative quantum theory of General Relativity. It is a background independent theory based on a description of the gravitational field in terms of…
Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a…
This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic…