Related papers: Gravity, Geometry and the Quantum
We feel that non-commutative geometry is to particle physics what Riemannian geometry is to gravity. We try to explain this feeling.
The occurrence of singularities where spacetime curvature becomes infinite and geodesic evolution breaks down are inevitable events in classical general relativity (GR) unless one chooses an exotic matter violating weak energy condition.…
The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity…
Caianiello's derivation of Quantum Geometry through an isometric embedding of the spacetime ({\bf M},\tilde{g}) in the pseudo-Riemannian structure ({\bf T^*M},g^*_{AB}) is reconsidered. In the new derivation, a non-linear connection and the…
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…
Starting from a new understanding of the vacuum energy problem based on the combination of the phase space regularization and the holographic bound, we argue that quantum gravity should be understood as gravitized quantum theory, that is,…
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…
General Theory of Relativity and Quantum theory gives two different description of the same mother nature in the big and small scale respectively. Mathematical languages of these two theories are entirely different, one is geometric while…
Quantum gravity is the missing piece in our understanding of the fundamental interactions today. Given recent observational breakthroughs in gravity, providing a quantum theory for what lies beyond general relativity is more urgent than…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
Loop quantum gravity introduces strong non-perturbative modifications to the dynamical equations in the semi-classical regime, which are responsible for various novel effects, including resolution of the classical singularity in a Friedman…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
A brief overview of loop quantum cosmology of homogeneous isotropic models is presented with emphasis on the origin of and subtleties associated with the resolution of big bang and big crunch singularities. These results bear out the…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…
Cosmology is built on a relativistic understanding of gravity, where the geometry of the Universe is dynamically determined by matter and energy. In the cosmological concordance model, gravity is described by General Relativity, and it is…
3-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly soluble under the assumption of axi-symmetry. The solution is used to probe several quantum gravity issues. In particular, it is shown that the quantum…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients…