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In this article we study two related models of quantum geometry: generic random trees and two-dimensional causal triangulations. The Hausdorff and spectral dimensions that arise in these models are calculated and their relationship with the…
Our conventional system of physical units is based on local or microscopic {\it dimensional} quantities which are {\it defined}, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may…
We consider 3+1 dimensional Quantum Field Theories (QFTs) coupled to the dilaton and the graviton. We show that the graviton-dilaton scattering amplitude receives a universal contribution which is helicity flipping and is proportional to…
We highlight the fact that the lack of scale invariance in the gravitational field equations of General Relativity results from the underlying assumption that the appropriate scale for the gravitational force should be linked to the atomic…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
We investigate the non-perturbative degrees of freedom of a class of weakly non-local gravitational theories that have been proposed as an ultraviolet completion of general relativity. At the perturbative level, it is known that the degrees…
We demonstrate the feasibility of a nonperturbative analysis of quantum field theory in the worldline formalism with the help of an efficient numerical algorithm. In particular, we compute the effective action for a super-renormalizable…
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental…
Quantum gravity effects are traditionally tied to short distances and high energies. In this essay we argue that, perhaps surprisingly, quantum gravity may have important consequences for the phenomenology of the infrared. We center our…
We study spectral properties of a non-Hermitian Hamiltonian describing a quantum particle propagating in a random imaginary scalar potential. Cast in the form of an effective field theory, we obtain an analytical expression for the ensemble…
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…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
We extend our analysis for scalar fields in a Robertson-Walker metric to the electromagnetic field and Dirac fields by the method of invariants. The issue of the relation between conformal properties and particle production is re-examined…
A hybrid model which allows to interpolate between the (original) Regge approach and dynamical triangulations is introduced. The gained flexibility in the measure is exploited to study dynamical triangulation in a fixed geometry. Our…
Quantum gravity can determine the dependence of gauge couplings in a scalar field, which is related to possible fifth forces and time varying fundamental "constants". This prediction is based on the scaling solution of functional flow…
Planck-scale dynamical dimensional reduction is attracting more and more interest in the quantum-gravity literature since it seems to be a model independent effect. However different studies base their results on different concepts of…
One of the main results of Scale Relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The Scale Relativity theory introduces an explicit dependence of…
We describe a non-perturbative approach to studying the gravitational collapse of a scalar field in spherical symmetry with quantum gravity corrections. Quantum effects are described by a phase space function that modifies the constraints…
The dynamical triangulations approach to quantum gravity is investigated in detail for the first time in five dimensions. In this case, the most general action that is linear in components of the f-vector has three terms. It was suspected…
Quantum scale invariant regularization is a variant of dimensional regularization where the renormalization scale is treated as a dynamical field. But, rather than be regarded as a novel regularization method on par with dimensional…