Related papers: The Unification of Classical and Quantum Gravity
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
Gravity is specifically the attractive force between two masses separated at a distance. Is this force a derived or a fundamental interaction? We believe that all fundamental interactions are quantum in nature but a derived interaction may…
A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Numerical simulations have given very interesting results in the cases of two, three and four…
We re-examine the nonperturbative curvature properties of two-dimensional Euclidean quantum gravity, obtained as the scaling limit of a path integral over dynamical triangulations of a two-sphere, which lies in the same universality class…
While quantum computing holds immense potential for tackling previously intractable problems, its current practicality remains limited. A critical aspect of realizing quantum utility is the ability to efficiently interface with data from…
Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are…
We present a brief description of the ``consistent discretization'' approach to classical and quantum general relativity. We exhibit a classical simple example to illustrate the approach and summarize current classical and quantum…
Improvement of the classical gravity with the running gravitational coupling obtained from asymptotically safe gravity, is a good way of considering the effects of quantum gravity. This is usually done for metric theories of gravity. Here…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
I review and discuss some recent developments in non-perturbative approaches to quantum gravity, with an emphasis on discrete formulations, and those coming from a classical connection description.
Affine quantum gravity, which differs notably from either string theory or loop quantum gravity, is briefly reviewed. Emphasis in this article is placed on the use of affine coherent states in this program.
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
We have recently introduced an approach for studying perturbatively classical and quantum canonical general relativity. The perturbative technique appears to preserve many of the attractive features of the non-perturbative quantization…
A new set of fundamental commutation relations (CR) for quantum gravity is presented. The basic variables are the eight components of the unimodular part of the spatial dreibein and eight SL(3,R) generators which correspond to Klauder's…
We present in detail a four-dimensional unified quantum theory. In this theory, we identify three class of parameters, coordinate-momentum, spin and gauge, as all and as the only fundamental parameters to describe quantum fields. The…
One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…
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,…
The FRT quantum group and space theory is reformulated from the standard mathematical basis to an arbitrary one. The $N$-dimensional quantum vector Cayley-Klein spaces are described in Cartesian basis and the quantum analogs of…