From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity

@article{Giesel2012FromCT,
  title={From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity},
  author={Kristina Giesel and H. Sahlmann},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2012}
}
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction is the inclusion of new proposals for coupling matter to gravity that can be used to deparametrize the theory, thus making its dynamics more tractable. The classical and quantum aspects of these new proposals are explained alongside the standard quantization… 
View PDF on arXiv
24 Citations
Highly Influential Citations
3
Background Citations
8
Methods Citations
2

24 Citations

An elementary introduction to loop quantum gravity
An introduction to loop quantum gravity is given, focussing on the fundamental aspects of the theory, different approaches to the dynamics, as well as possible future directions. It is structured in…
A review on Loop Quantum Gravity
The aim of this dissertation is to review `Loop Quantum Gravity', explaining the main structure of the theory and indicating its main open issues. We will develop the two main lines of research for…
Cosmological effective Hamiltonian from full loop quantum gravity dynamics
Towards the fundamental spectrum of the quantum Yang-Mills theory
In this work we focus on the quantum Einstein-Yang-Mills sector quantized by the methods of loop quantum gravity. We point out the improved UV behavior of the coupled system as compared to pure…
Loop quantum cosmology from an alternative Hamiltonian
In this paper, a new Hamiltonian constraint operator for loop quantum cosmology is constructed by using the Chern-Simons action. The quantum dynamics of the $k=0$ cosmological model with respect to a…
Solvable model for quantum gravity?
We study a type of geometric theory with a non-dynamical 1-form field. Its dynamical variables are an su(2) gauge field and a triad of su(2) valued 1-forms. Hamiltonian decomposition reveals that the…
QFT on quantum spacetime: a compatible classical framework
(Dated: May 21, 2013)We develop a systematic classical framework to accommodate canonical quantization of geomet-ric and matter perturbations on a quantum homogeneous isotropic flat spacetime. The…
Loop quantum cosmology from an alternative Hamiltonian. II. Including the Lorentzian term
The scheme of using the Chern-Simons action to regularize the gravitational Hamiltonian constraint is extended to including the Lorentzian term in the $k=0$ cosmological model. The Euclidean term and…
Introduction to SU(2) recoupling theory and graphical methods for loop quantum gravity
We present a pedagogical introduction to SU(2) recoupling theory, focusing on those aspects of the topic which are useful for practical calculations in loop quantum gravity. In particular, we give a…
Canonical Quantum Gravity, Constructive QFT, and Renormalisation
The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously…
...
...

References

SHOWING 1-10 OF 124 REFERENCES
Gravity quantized: Loop quantum gravity with a scalar field
...''but we do not have quantum gravity.'' This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact,…
New variables for classical and quantum gravity in all dimensions: III. Quantum theory
We quantize the new connection formulation of (D + 1)-dimensional general relativity developed in our companion papers by loop quantum gravity (LQG) methods. It turns out that all the tools prepared…
The Length operator in Loop Quantum Gravity
Quantum gravity as a “sum over surfaces”
Loop quantum gravity vacuum with nondegenerate geometry
In loop quantum gravity, states of the gravitational field turn out to be excita- tions over a vacuum state that is sharply peaked on a degenerate spatial geometry. While this vacuum is singled out…
New variables for classical and quantum gravity.
  • Ashtekar
  • Physics
    Physical review letters
  • 1986
TLDR
A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced that enables one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory.
Towards loop quantum gravity without the time gauge.
TLDR
The Hamiltonian formulation of the Holst action is reviewed and it provides a solution of second-class constraints corresponding to a generic local Lorentz frame that emphasizes that the loop quantum gravity quantization procedure can be applied when the time-gauge condition does not stand.
Loop quantum gravity - a short review
In this article we review the foundations and the present status of loop quantum gravity. It is short and relatively non-technical, the emphasis is on the ideas, and the flavor of the techniques. In…
Loop Quantum Gravity
TLDR
An overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity is given, and a guide to the relevant literature is given.
Introductory lectures to loop quantum gravity
We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete…
...
...