Introduction to Modern Canonical Quantum General Relativity

By T. Thiemann. 2001

705 citations recorded by the source corpus.

This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the fact that the quantum theory is based on formulating classical general relativity as a theory of connections rather than metrics as compared to in original version due to Arnowitt, Deser and Misner. Canonical quantum general relativity is an attempt to define a mathematically rigorous, non-perturbative, background independent theory of Lorentzian quantum gravity in four spacetime dimensions in the continuum. The approach is minimal in that one simply analyzes the logical consequences of combining the principles of general relativity with the principles of quantum mechanics. The requirement to preserve background independence has lead to new, fascinating mathematical structures which one does not see in perturbative approaches, e.g. a fundamental discreteness of spacetime seems to be a prediction of the theory providing a first substantial evidence for a theory in which the gravitational field acts as a natural UV cut-off. An effort has been made to provide a self-contained exposition of a restricted amount of material at the appropriate level of rigour which at the same time is accessible to graduate students with only basic knowledge of general relativity and quantum field theory on Minkowski space.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/983512a7ca45f7bfacc600751ca116b3669675c9

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Citations in the corpus

SU(2) loop quantum gravity seen from covariant theory (2002, background): “Also at V.A. Fock Department of Theoretical Physics, St. Petersburg University, Russia †e.mail: livine@cpt.univ-mrs.fr”
Lectures on Loop Quantum Gravity (2002, background): “ globally deﬁned. In fact, for the case of G= SU(2) and dim(σ) = 3 one can show that the ﬁbre bundle is necessarily trivial but for the generalization to the generic case we again refer the reader to [1]. With these remrks out of the way we may begin by deﬁning a polarization. The fact that GR has b”
The case for background independence (2005, background): “But why should we mod out by diffeomorphisms? As Einstein intuited in his famous “hole argument”, and Dirac codified, one must mod out by diffeomorphisms if one is to have deterministic evolution from initial data[8, 13, 38].”
Spherically symmetric quantum geometry: Hamiltonian constraint (2005, background): “obtained so far mainly in homogeneous models. New applications in particular of the spherically symmetric model in the context of black hole physics are discussed. 1 Introduction Loop quantum gravity [1, 2, 3] provides a candidate for a non-perturbative, background independent quantization of genera”
Loop quantum gravity: an outside view (2005, background): “The number of ambiguities can be reduced by invoking independence of the spatial background [11], and indeed, without making such choices, one would not even obtain sensible expressions, as we shall see very explicitly.”
Corrections to the Friedmann equations from loop quantum gravity for a universe with a free scalar field (2008, background): “Loop Quantum Gravity (see [1-3] for reviews) is a nonperturbative approach to the problem of quantizing gravity.”
Thermodynamical Aspects of Gravity: New insights (2009, background): “While string theory tries to incorporate all interactions in a unified manner, loop quantum gravity [89, 90] has the limited goal of providing a canonically quantized version of Einstein gravity.”
FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY (2005, background): “ruction. This motivates us to deﬁne the connection Aa i = Γ i a + γKi a. Moreover, the transformation from the 19 pair (Eea i ,K j b) to (Pea i ,Ab) can be proved to be a canonical transformation [29][122], i.e., the Poisson algebra of the basic dynamical variables is preserved under the transformat”
Loop quantum cosmology and slow roll inflation (2009, background): “The origin of this resolution lies in the quantum geometry effects that are at the heart of loop quantum gravity [26, 27, 28].”
Gravity and the thermodynamics of horizons (2005, background): “While string theory tries to incorporate all interactions in a unified manner, loop quantum gravity [126,127] has the limited goal of providing a canonically quantised version of Einstein gravity.”
Loop quantum cosmology: a status report (2011, methodology): “A convenient basis in Htotal kin is provided by the so-called spin network states [26, 35, 36, 135, 136].”
Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation (2002, methodology): “For an introduction to the formalism of QGR as a whole, we refer the reader to [3, 2] or to the brief introduction in [1].”