Abstract
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.
Highlights
For around 100 years1 of constantly branching research, the landscape of quantum gravity investigations has become very broad and diverse
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
One possible realization of such a taxonomy of classical and quantum gravity has been depicted in Fig. 1 but it should be understood as an outline rather than a precise diagram
Summary
For around 100 years of constantly branching research, the landscape of quantum gravity investigations has become very broad and diverse. In order to explore all of these possibilities we should employ a more architectural way of thinking, by which we mean trying to uncover the hypothetical structure of the still incomplete theory and to understand its internal functions This contrasts with what may be called the engineering approach, in which independent groups of researchers keep working on their rival theories and which has dominated quantum gravity over the years. In order to represent the structure and phenomena of the discussed theory we will apply the idea of a mind map The nodes of such a graph (playing the role of bricks) will denote different models of quantum gravity as well as their features and known results.
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