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After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical continuous space-time required conceptually new approach. We present briefly three proposals: loop quantum gravity (LQG), the field-theoretic framework on noncommutative space-time and QG models formulated on discretized (triangularized) space-time. We evaluate these models as realizing expected important properties of QG: background independence, consistent quantum diffeomorphisms, noncommutative or discrete structure of space-time at very short distances, finite/renormalizable QG corrections. We only briefly outline an important issue of embedding QG into larger geometric and dynamical frameworks (e.g. supergravity, (super)strings, p-branes, M-theory), with the aim to achieve full unification of all fundamental interactions.
We study random walks on ensembles of a specific class of random multigraphs which provide an effective graph ensemble for the causal dynamical triangulation (CDT) model of quantum gravity. In particular, we investigate the spectral dimension of the
In a series of comments, Bonder et al. criticized our work on decoherence due to time dilation [Nature Physics 11, 668-672 (2015)]. First the authors erroneously claimed that our results contradict the equivalence principle, only to resolve the alleg
This conference summary and outlook provides a personal overview of the topics and themes of the August 2009 Dresden meeting on quantum criticality and novel phases. The dichotomy between the local moment and the itinerant views of magnetism is revis
In recent years several approaches to quantum gravity have found evidence for a scale dependent spectral dimension of space-time varying from four at large scales to two at small scales of order of the Planck length. The first evidence came from nume
We investigate the underlying quantum group symmetry of 2d Liouville and dilaton gravity models, both consolidating known results and extending them to the cases with $mathcal{N} = 1$ supersymmetry. We first calculate the mixed parabolic representati