Related papers: Fundamentals of Quantum Gravity
A sketch of a recent approach to quantum gravity is presented which involves several unconventional aspects. The basic ingredients include: (1) Affine kinematical variables; (2) Affine coherent states; (3) Projection operator approach for…
Affine quantum gravity involves (i) affine commutation relations to ensure metric positivity, (ii) a regularized projection operator procedure to accomodate first- and second-class quantum constraints, and (iii) a hard-core interpretation…
A sketch of the affine quantum gravity program illustrates a different perspective on several difficult issues of principle: metric positivity; quantum anomalies; and nonrenormalizability.
The main principle of affine quantum gravity is the strict positivity of the matrix \{\hat g_{ab}(x)\} composed of the spatial components of the local metric operator. Canonical commutation relations are incompatible with this principle,…
The central principle of affine quantum gravity is securing and maintaining the strict positivity of the matrix $\{\hg_{ab}(x)\}$ composed of the spatial components of the local metric operator. On spectral grounds, canonical commutation…
The basic features of the complex canonical formulation of general relativity and the recent developments in the quantum gravity program based on it are reviewed. The exposition is intended to be complementary to the review articles…
In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to…
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
All attempts to quantize gravity face several difficult problems. Among these problems are: (i) metric positivity (positivity of the spatial distance between distinct points), (ii) the presence of anomalies (partial second-class nature of…
The basic principles of Affine Quantum Gravity are presented in a pedagogical style with a limited number of equations.
In a remarkable paper, T. Koslowski introduced kinematical representations for loop quantum gravity in which there is a non-degenerate spatial background metric present. He also considered their properties, and showed that Gauss and…
Recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non-classical modification of the ground state wave function leads to a result that eliminates term-by-term divergences that arise in a…
I briefly review the current status of quantum gravity. After giving some general motivations for the need of such a theory, I discuss the main approaches in quantizing general relativity: Covariant approaches (perturbation theory,…
We provide a brief overview of what is known about Quadratic Gravity, which includes terms quadratic in the curvatures in the fundamental action. This is proposed as a renormalizeable UV completion for quantum gravity which continues to use…
The topic of quantum reference frames (QRFs) has attracted a great deal of attention in the recent literature. Potentially, the correct description of such frames is important for both the technological applications of quantum mechanics and…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
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…
An affine quantization approach leads to a genuine quantum theory of general relativity by extracting insights from a short list of increasingly more complex, soluble, perturbably nonrenormalizable models.
Review of the most basic issues appearing in the most conservative approaches to quantum theory of gravity is given. The most part of the review is devoted to issues of perturbative quantization based on functional integral technique.…