Related papers: Scaling and Renormalization in two dimensional Qua…

It is well known that standard gauge theories are renormalizable in D=4 while Einstein gravity is renormalizable in D=2. This is where the research in the field of two derivatives theories is currently standing. We hereby present a class of…

The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously non-polynomial character of the…

Originating in theoretical physics, Liouville quantum gravity (LQG) has been an important topic in probability theory and mathematical physics in the past two decades. In this proceeding, we review two aspects of this topic. The first is…

We make some remarks on the group of symmetries in gravity; we believe that K-theory and noncommutative geometry inescepably have to play an important role. Furthermore we make some comments and questions on the recent work of Connes and…

We evaluate the quantum corrections of the Einstein-Hilbert action with boundaries in the $2+\epsilon$ dimensional expansion approach. We find the Einstein-Hilbert action with boundaries to be renormalizable to the one loop order. We…

Lorentzian simplicial quantum gravity is a non-perturbatively defined theory of quantum gravity which predicts a positive cosmological constant. Since the approach is based on a sum over space-time histories, it is perturbatively…

We review the techniques used to renormalize quantum field theories at several loop orders. This includes the techniques to systematically extract the infinities in a Feynman integral and the implementation of the algorithm within computer…

We propose a renormalization prescription for the Wheeler-DeWitt equation of (3+1)-dimensional Einstein gravity and also propose a strong coupling expansion as an approximation scheme to probe quantum geometry at length scales much smaller…

We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…

In a perturbative approach Einstein-Hilbert gravity is quantized about a flat background. In order to render the model power counting renormalizable, higher order curvature terms are added to the action. They serve as Pauli-Villars type…

We use the duality between the local Cartezian coordinates and the solutions of the Klein-Gordon equation to parametrize locally the spacetime in terms of wave functions and prepotentials. The components of metric, metric connection,…

We show how to reliably calculate quantum gravitational corrections to cosmological models using the unique effective action formalism for quantum gravity. Our calculations are model independent and apply to any ultra-violet complete theory…

Using the recently found first order formulation of two-dimensional dilaton gravity with boundary, we perform a Hamiltonian analysis and subsequent path integral quantization. The importance of the boundary terms to obtain the correct…

In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…

We focus on the use of the functional Wilsonian renormalization group framework characterized by a proper time regulator and test its use in the search of the scaling solutions and the critical properties of an O(N)-invariant scalar field…

We evaluate the three point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions…

The exact renormalization group equation for pure quantum gravity is derived for an arbitrary gauge parameter in the space-time dimension $d=4$. This equation is given by a non-linear functional differential equation for the effective…

Applying recursive renormalization group transformations to a scalar field theory, we obtain an effective quantum gravity theory with an emergent extra dimension, described by a dual holographic Einstein-Klein-Gordon type action. Here, the…

In the framework of dimensional regularization, we propose a generalization of the renormalization group equations in the case of the perturbative quantum gravity that involves renormalization of the metric and of the higher order Riemann…

The anomalous dimensions of the Planck mass and the cosmological constant are calculated in a renormalizable quantum conformal gravity with a single dimensionless coupling, which is formulated using dimensional regularization on the basis…