Related papers: Summing over spacetime dimensions in quantum gravi…
The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological constant. We present the evidence…
We present the elements of resummed quantum gravity, a new approach to quantum gravity based on the work of Feynman using the simplest example of a scalar field as the representative matter. We show that we get a UV finite quantum…
A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional. I review this evidence, starting with a discussion of the physical meaning…
Recently there have been several studies devoted to the investigation of the fate of fundamental relativistic symmetries at the foreseen unification of gravity and quantum regime, that is the Planck scale. In order to preserve covariance of…
We employ the graviton self-energy induced by a massless, minimally coupled (MMC) scalar on de Sitter background to compute the quantum corrections to the gravitational potentials of a static point particle with a mass $M$. The…
We develop the general formalism for performing perturbative diagrammatic expansions in the lattice theory of quantum gravity. The results help establish a precise correspondence between continuum and lattice quantities, and should be a…
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However,…
Quantum gravitational corrections to the effective potential, at one-loop level and in the leading-log approximation, for scalar quantum electrodynamics with higher-derivative gravity ---which is taken as an effective theory for quantum…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
The Feynman propagator in curved spacetime admits an asymptotic (Schwinger-DeWitt) series expansion in derivatives of the metric. Remarkably, all terms in the series containing the Ricci scalar R can be summed exactly. We show that this…
We discuss the notion of causality in Quantum Gravity in the context of sum-over-histories approaches, in the absence therefore of any background time parameter. In the spin foam formulation of Quantum Gravity, we identify the appropriate…
We consider summations over digamma and polygamma functions, often with summands of the form (\pm 1)^n\psi(n+p/q)/n^r and (\pm 1)^n\psi^{(m)} (n+p/q)/n^r, where m, p, q, and r are positive integers. We develop novel general integral…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
The generalized $f(R)$ gravity with curvature-matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal spacelike Killing vector field of 5D spacetime, and it can be reduced to the 4D…
The quantum contributions to the gravitational action are relatively easy to calculate in the higher derivative sector of the theory. However, the applications to the post-inflationary cosmology and astrophysics require the corrections to…
Recent models for discrete euclidean quantum gravity incorporate a sum over simplicial triangulations. We describe an algorithm for simulating such models in general dimensions. As illustration we show results from simulations in four…
The notions of minimum geometrical length and minimum length scale are discussed with reference to correlation functions obtained from in-in and in-out amplitudes in quantum field theory. Whereas the in-in propagator for metric…
The macroscopic dimensions of space should not be input but rather output of a general model for physics. Here, dimensionality arises from a recently discovered mathematical bifurcation: positive versus indefinite manifold pairings. It is…
As it stands, quantum gravity coupled with matter in three spacetime dimensions is not finite. In this paper I show that an algorithmic procedure that makes it finite exists, under certain conditions. To achieve this result, gravity is…