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Curved geometry and Graphs

Published 14 Oct 2011 in gr-qc | (1110.3278v3)

Abstract: Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a particle hopping on the graph. We discuss the role of connectivity in emergent Lorentzian perturbations in a curved background and the Bose--Hubbard (BH) model defined on graphs with particular symmetries.

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