Related papers: Fundamental Structure of Loop Quantum Gravity
We present a generalization of the first-order formalism used to describe the dynamics of a classical system. The generalization is then applied to the first-order action that describes General Relativity. As a result we obtain equations…
Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual…
We present a pedagogical introduction to the notions underlying the connection formulation of General Relativity - Loop Quantum Gravity (LQG) - with an emphasis on the physical aspects of the framework. We begin by reviewing General…
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…
We review uniqueness results for the kinematical part of loop quantum gravity. After sketching the general loop formalism, the holonomy-flux and the Weyl algebras are introduced. In both cases, then, diffeomorphism invariant representations…
General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…
Loop Quantum Gravity (LQG) is a promising approach to quantum gravity, in particular because it is based on a rigorous quantization of the kinematics of gravity. A difficult and still open problem in the LQG program is the construction of…
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…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
We present a systematic approach to the kinematics of quantum-reduced loop gravity, a model originally proposed by Alesci and Cianfrani as an attempt to probe the physical implications of loop quantum gravity. We implement the quantum…
After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical continuous space-time required conceptually new approach. We…
We discuss a covariant setting for Hamiltonian formalism in a relativistic field theory and we use this to obtain again the properties of Hamilton principal functional in Newtonian mechanics, relativistic mechanics, Klein-Gordon,…
Loop Quantum Gravity is a nonperturbative and background independent program for the quantization of General Relativity. Its underlying formalism has been applied successfully to the study of cosmological spacetimes, both to test the…
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine…
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic…
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
We review quantum gravity model building using the new formalism of `quantum Riemannian geometry' to construct this on finite discrete spaces and on fuzzy ones such as matrix algebras. The formalism starts with a `differential structure' as…
The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity (LQG) is a promising proposal for…
An outstanding open issue in our quest for physics beyond Einstein is the unification of general relativity (GR) and quantum physics. Loop quantum gravity (LQG) is a leading approach toward this goal. At its heart is the central lesson of…