Related papers: Recent Developments in Non-Perturbative Quantum Gr…
We investigate some properties of geometric operators in canonical quantum gravity in the connection approach \`a la Ashtekar, which are associated with volume, area and length of spatial regions. We motivate the construction of analogous…
The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously…
We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four spacetime dimensions in the continuum in a spin-network basis. We also display a new technique of regularization…
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…
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general…
Research during the last decade demonstrates that effects originating on the Planck scale are currently being tested in multiple observational contexts. In this review we discuss quantum gravity phenomenological models and their possible…
A realistic measurement-free theory for the quantum physics of multiple qubits is proposed. This theory is based on a symbolic representation of a fractal state-space geometry which is invariant under the action of deterministic and locally…
The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non- degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG…
A new representation for canonical gravity and supergravity is presented, which combines advantages of Ashtekar's and the Wheeler~DeWitt representation: it has a nice geometric structure and the singular metric problem is absent. A formal…
This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby enabling a detailed comparison of results in…
We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framework, the vacuum is peaked on flat connections, and states…
The recently proposed loop representation, used previously to find exact solutions to the quantum constraints of general relativity, is here used to quantize linearized general relativity. The Fock space of graviton states and its…
The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…
We construct physical semi-classical states annihilated by the Hamiltonian constraint operator in the framework of loop quantum cosmology as a method of systematically determining the regime and validity of the semi-classical limit of the…
Being able to perform explicit computations in a nonperturbative, Planckian regime is key to understanding quantum gravity as a fundamental theory of gravity and spacetime. Rather than a variety of different approaches to quantum gravity,…
An open issue in loop quantum gravity (LQG) is the introduction of a non-vanishing cosmological constant $\Lambda$. In 3d, Chern-Simons theory provides some guiding lines: $\Lambda$ appears in the quantum deformation of the gauge group. The…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…