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Is there an approach to quantum gravity which is conceptually simple, relies on very few fundamental physical principles and ingredients, emphasizes geometric (as opposed to algebraic) properties, comes with a definite numerical approximation scheme, and produces robust results, which go beyond showing mere internal consistency of the formalism? The answer is a resounding yes: it is the attempt to construct a nonperturbative theory of quantum gravity, valid on all scales, with the technique of so-called Causal Dynamical Triangulations.
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see, for example, U. Jacob and T. Piran: Neutrinos from gamma-ray bursts as a tool to explore quantum-gravity-induced Lorentz violation
2007
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M. Niedermaier: The asymptotic safety scenario in quantum gravity: An introduction
2007
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D. Benedetti, R. Loll and F. Zamponi: (2+1)-dimensional quantum gravity as the continuum limit of causal dynamical triangulations
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D. Benedetti and R. Loll: Unexpected spin-off from quantum gravity
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J. Ambjørn, A. Goerlich, J. Jurkiewicz and R. Loll: Planckian birth of the quantum de Sitter universe
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