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There is a beautiful theory of quantum gravity called "Canonical Quantum Graivty" which aims to quantized general relativity using typical canonical methods (canonical quantization/path integral formulation). This theory predicts a granular structure to spacetime while maintaining local lorentz invariance. The theory gives a spectrum of eigenvalues for quantized area and volume based on Penrose's spin-network graphs, except the theory consideres equivilence classes of spin-networks under diffeomorphisms. The Path-integral formulation of the theory consists in considering a sum-over-geometries which is entirely background independent, carried out in sum over 2-complexes, which are themselves graphs. Here is a small set of lectures that might interest you: http://arxiv.org/abs/1102.3660

Response to comment by OP: There are no experimental tests of quantum gravity that we know as of now, whether because we don't know how to interpret what we already have in front of us, or because we simply don't have the technical power/creativity yet, although there are a number of new papers that suggest experiments that may be done at the LHC for Canonical Quantum Gravity, which have to do with the evaporation of micro-black holes and their radiation spectra which differs the classical spectra predicted by QFT in curved spacetime. Canonical Quantum Gravity is also the only mainstream theory of QG on the table that gives falsifiable, numerical predictions that are novel; at least I have yet to see anything else on the forums and arxiv that does, so that doesn't mean much.

There is a beautiful theory of quantum gravity called "Canonical Quantum Graivty" which aims to quantized general relativity using typical canonical methods (canonical quantization/path integral formulation). This theory predicts a granular structure to spacetime while maintaining local lorentz invariance. The theory gives a spectrum of eigenvalues for quantized area and volume based on Penrose's spin-network graphs, except the theory consideres equivilence classes of spin-networks under diffeomorphisms. The Path-integral formulation of the theory consists in considering a sum-over-geometries which is entirely background independent, carried out in sum over 2-complexes, which are themselves graphs. Here is a small set of lectures that might interest you: http://arxiv.org/abs/1102.3660

There is a beautiful theory of quantum gravity called "Canonical Quantum Graivty" which aims to quantized general relativity using typical canonical methods (canonical quantization/path integral formulation). This theory predicts a granular structure to spacetime while maintaining local lorentz invariance. The theory gives a spectrum of eigenvalues for quantized area and volume based on Penrose's spin-network graphs, except the theory consideres equivilence classes of spin-networks under diffeomorphisms. The Path-integral formulation of the theory consists in considering a sum-over-geometries which is entirely background independent, carried out in sum over 2-complexes, which are themselves graphs. Here is a small set of lectures that might interest you: http://arxiv.org/abs/1102.3660

Response to comment by OP: There are no experimental tests of quantum gravity that we know as of now, whether because we don't know how to interpret what we already have in front of us, or because we simply don't have the technical power/creativity yet, although there are a number of new papers that suggest experiments that may be done at the LHC for Canonical Quantum Gravity, which have to do with the evaporation of micro-black holes and their radiation spectra which differs the classical spectra predicted by QFT in curved spacetime. Canonical Quantum Gravity is also the only mainstream theory of QG on the table that gives falsifiable, numerical predictions that are novel; at least I have yet to see anything else on the forums and arxiv that does, so that doesn't mean much.

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There is a beautiful theory of quantum gravity called "Canonical Quantum Graivty" which aims to quantized general relativity using typical canonical methods (canonical quantization/path integral formulation). This theory predicts a granular structure to spacetime while maintaining local lorentz invariance. The theory gives a spectrum of eigenvalues for quantized area and volume based on Penrose's spin-network graphs, except the theory consideres equivilence classes of spin-networks under diffeomorphisms. The Path-integral formulation of the theory consists in considering a sum-over-geometries which is entirely background independent, carried out in sum over 2-complexes, which are themselves graphs. Here is a small set of lectures that might interest you: http://arxiv.org/abs/1102.3660