Background independent quantum gravity: A Status report

By Abhay Ashtekar, J. Lewandowski. 2004

1,573 citations recorded by the source corpus.

The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the review should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the review is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well-established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the review to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/729db4a7fc6fb3f0d9eb7f2af28b269b2183c1dc

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Citations in the corpus

Phase space descriptions for simplicial 4D geometries (2008, background): “In many approaches to quantum gravity, such as loop quantum gravity [2], quantum Regge calculus [3, 4] and causal dynamical triangulations [5], discrete models of space–time appear in one form or another.”
Loop quantum cosmology of Bianchi type IX models (2009, background): “Loop quantum cosmology (LQC) [1, 2] is an approach to quantum cosmology following the ideas of loop quantum gravity (LQG) [3–5].”
Spin-foams for all loop quantum gravity (2009, background): “(ii) The surface approach [1] (see Rovelli’s book) and [24, 26], within which one considers a manifold M and spin-network states s ∈ H defined by the spin-networks embedded in ∂M = .”
Flipped spinfoam vertex and loop gravity (2007, methodology): “We will use a method essentially coming from that described in [49], and briefly mentioned in [2]; the method is the following.”
Introduction to loop quantum gravity and spin foams (2004, background): “The solution to the previous equation can be written explicitly in terms of the triad components Γa = − 1 2 ǫijke b j ( ∂[ae k b] + δ δmse c l e m a ∂be s c ) , (19)”
Quantum nature of the big bang: An analytical and numerical investigation (2006, methodology): “Sq ∗Electronic address: ashtekar@gravity.psu.edu †Electronic address: pawlowsk@gravity.psu.edu ‡Electronic address: singh@gravity.psu.edu I. INTRODUCTION Loop quantum gravity (LQG) is a background independent, non-perturbative approach to quantum gravity [1, 2, 3].”
Anomaly freedom in perturbative loop quantum gravity (2008, neutral): “39 29 v1 [ gr -q c] 2”
The Spin-Foam Approach to Quantum Gravity (2012, methodology): “If we include the scalar constraint, the remaining Poisson brackets are {S(N), V (N)} = −S(LNN), (54) and finally {S(N), S(M)} = V (S) + terms proportional to the Gauss constraint, (55) where, for simplicity, we are ignoring the terms proportional to the Gauss law (the complete expression can be fou”
Zakopane lectures on loop gravity (2011, background): “The two quantities~Ll and Uσ are the basis of the canonical loop quantization of general relativity [113, 4, 82].”
Loop quantum gravity: an outside view (2005, background): “While Hkin is non-separable, it is expected that Hdiff is separable [134, 135] provided one averages over homeomorphisms rather than diffeomorphisms (if one divides out only by analytic or C∞ diffeomorphisms, Hdiff remains non-separable, see also [12] for a recent discussion of this point).”
The pre-inflationary dynamics of loop quantum cosmology: confronting quantum gravity with observations (2012, background): “What is the status of the ‘trans-Planckian issue’ which, in heuristic discussions, is often associated with modes of trans-Planckian frequencies? Recall, first, that the quantum Riemannian geometry underlying LQG is subtle [49, 50].”