Towards the map of quantum gravity. (English) Zbl 1392.83078
Summary: In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Hořava-Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful
in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.
MSC:
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C45 | Quantization of the gravitational field |
| 83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
| 83-02 | Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory |
Keywords:
causal dynamical triangulations; Hořava-Lifshitz gravity; asymptotic safety; loop quantum gravity; deformations of relativistic symmetries; phase diagram; spectral dimensionReferences:
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