Related papers: Canonical Quantum Gravity
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…
The idea that quantum gravity manifestations would be associated with a violation of Lorentz invariance is very strongly bounded and faces serious theoretical challenges. Other related ideas seem to be drowning in interpretational…
This Chapter provides an up to date, pedagogical review of some of the most relevant advances in loop quantum cosmology. We review the quantization of homogeneous cosmological models, their singularity resolution and the formulation of…
Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
We discuss the canonical treatment and quantization of matter coupled supergravity in three dimensions, with special emphasis on $N=2$ supergravity. We then analyze the quantum constraint algebra; certain operator ordering ambiguities are…
After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of…
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…
The geometric foundations of General Relativity are revisited, with particular attention to its gauge invariance, as a key to understanding the true nature of spacetime. Beyond the common image of spacetime as a deformable 'fabric' filling…
We shall present here the causal interpretation of canonical quantum gravity in terms of new variables. Then we shall apply it to the minisuperspace of cosmology. A vacuum solution of quantum cosmology is obtained and the Bohmian trajectory…
We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions. Starting from the usual point particle action in the first order formalism, we introduce auxiliary variables which make the action locally…
We study embedding gravity, a modified theory of gravity, in which our space-time is assumed to be a four-dimensional surface in flat ten-dimensional space. Based on a simple geometric idea, this theory can be reformulated as General…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the…
A sketch of the affine quantum gravity program illustrates a different perspective on several difficult issues of principle: metric positivity; quantum anomalies; and nonrenormalizability.
With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…
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…
The bare bones of a theory of quantum gravity are exposed. It may have the potential to solve the cosmological constant problem. Less certain is its behavior in the Newtonian limit.
This is an introductory set of lecture notes on quantum cosmology, given in 1995 to an audience with interests ranging from astronomy to particle physics. Topics covered: 1. Introduction: 1.1 Quantum cosmology and quantum gravity; 1.2 A…
This chapter focuses on the status of the implementation of the dynamics in the canonical version of Loop Quantum Gravity (LQG). Concretely this means to provide a mathematical meaning of the quantum Einstein equations, sometimes called…