Related papers: Introductory lectures to loop quantum gravity
We consider a quantum field theory on a spherically symmetric quantum space time described by loop quantum gravity. The spin network description of space time in such a theory leads to equations for the quantum field that are discrete. We…
We discuss some of the issues to be addressed in arriving at a definitive noncommutative Riemannian geometry that generalises conventional geometry both to the quantum domain and to the discrete domain. This also provides an introduction to…
Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and 4-dimensional generally covariant physics. We…
We study a tentative generally covariant quantum field theory, denoted the T-Theory, as a tool to investigate the consistency of quantum general relativity. The theory describes the gravitational field and a minimally coupled scalar field;…
This is my Th\`ese d'Habilitation (HDR) on the topic of spinfoam models for quantum gravity, which I presented in l'Ecole Normale Sup\'erieure de Lyon on december 16 2010. The spinfoam framework is a proposal for a regularized path integral…
The implementation of the dynamics in loop quantum gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We find an…
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a…
By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear…
These Lecture Notes provide an elementary introduction to the quantization of two-dimensional quantum gravity. Nothing beyond undergratuate physics and mathematic is required. Explicit formulas for the partition functions for universes with…
We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability…
The 4-dimensional metric $f(\R)$ theories of gravity are cast into connection-dynamical formalism with real $\SU(2)$-connections as configuration variables. Through this formalism, the classical metric $f(\R)$ theories are quantized by…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
The spinfoam framework is a proposal for a regularized path integral for quantum gravity. Spinfoams define quantum space-time structures describing the evolution in time of the spin network states for quantum geometry derived from Loop…
This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems. Contents: 1. Introduction 2. Effective Field Theories 3. Low-Energy Quantum Gravity 4. Explicit Quantum…
I discuss the role played by the spin-network basis and recoupling theory (in its graphical tangle-theoretic formulation) and their use for performing explicit calculations in loop quantum gravity. In particular, I show that recoupling…
We show that loop gravity can equally well be formulated in in terms of spinorial variables (instead of the group variables which are commonly used), which have recently been shown to provide a direct link between spin network states and…
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental…
`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…
Multi-messenger astronomy provides us with the possibility of discovering phenomenological signatures of quantum-gravity effects. This should be of paramount importance in the pursuit of an elusive quantum theory for the gravitational…
In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms of the holonomy-flux variables, and show how it is related to the continuous phase space of general relativity. In particular, we prove…