Related papers: Step-by-Step Canonical Quantum Gravity -- Part I: …
The preceding talks given at this conference have dealt mainly with general ideas for, main problems of and techniques for the task of quantizing gravity canonically. Since one of the major motivations to arrange for this meeting was that…
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…
The main purpose of this paper is to analyse the earliest work of L\'eon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld…
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental…
The questions I have been asked during the 5th International School on Field Theory and Gravitation, have compelled me to give an account of the premises that I consider important for a beginner's approach to Loop Quantum Gravity. After a…
The method of solution of the initial value constraints for pure canonical gravity in terms of Ashtekar's new canonical variables due to CDJ is further developed in the present paper. There are 2 new main results : 1) We extend the method…
This paper presents a novel path integral formalism for Einstein's theory of gravitation from the viewpoint of optimal control theory. Despite its close relation to the well-known variational principles of physicists, optimal control turns…
We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of…
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of Covariant Quantum-Gravity (CQG-theory). The treatment is founded on the recently-identified Hamiltonian structure…
We construct a new vacuum for loop quantum gravity, which is dual to the Ashtekar-Lewandowski vacuum. Because it is based on BF theory, this new vacuum is physical for $(2+1)$-dimensional gravity, and much closer to the spirit of spin foam…
Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out.…
The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation…
This bibliography attempts to give a comprehensive overview of all the literature related to the Ashtekar connection and the Rovelli-Smolin loop variables. The original version was compiled by Peter H\"ubner in 1989, and it has been…
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…
Ashtekar's formulation for canonical quantum gravity is known to possess the topological solutions which have their supports only on the moduli space $\CN$ of flat $SL(2,C)$ connections. We show that each point on the moduli space $\CN$…
One of the main motivations behind so-called topos physics, as developed by Chris Isham and Andreas Doering [4-7], is to provide a framework for new theories of quantum gravity. In this article we do not search for such theories, but ask…
After a long technical and consequently philosophical disgression about the necessity of the construction presented in this book, a logically consistent and precise theory of quantum gravity is presented. The construction of this theory…
We perform canonical quantization of General Relativity, as an effective quantum field theory below the Planck scale, within the BRST-invariant framework. We show that the promotion of constraints to dynamical equations of motion for…
The goal of this article is to present a broad perspective on quantum gravity for \emph{non-experts}. After a historical introduction, key physical problems of quantum gravity are illustrated. While there are a number of interesting and…
New results from the new variables/loop representation program of nonperturbative quantum gravity are presented, with a focus on results of Ashtekar, Rovelli and the author which greatly clarify the physical interpretation of the quantum…