Related papers: Quantum Gravity is Renormalizable near Two Dimensi…
General two-dimensional pure dilaton-gravity can be discussed in a unitary way by introducing suitable field redefinitions. The new fields are directly related to the original spacetime geometry and in the canonical picture they generalize…
For any fundamental quantum field theory, unitarity, renormalizability, and relativistic invariance are considered to be essential properties. Unitarity is inevitably connected to the probabilistic interpretation of the quantum theory,…
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…
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…
Real-Space renormalization group techniques are developed for tackling large curvature fluctuations in quantum gravity. Within cells of invariant volume $a^4$, only certain types of fluctuations are allowed. Normal coordinates are used to…
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
We describe an approach to the quantisation of (2+1)-dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q-commutation relation. Solutions of diagonal and…
The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited. A proposal consisting of a specific re-normalization {\bf Assumption} and an accompanying {\bf Requirement} is put forward,…
We study the quantum aspects of the conformal gravity in four dimensions, specifically addressing a known discrepancy in beta functions between general quadratic curvature theories and conformal gravity, which corresponds to two scalar…
This article provides a cartoon of the quantization of General Relativity using the ideas of effective field theory. These ideas underpin the use of General Relativity as a theory from which precise predictions are possible, since they show…
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…
The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an…
A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies…
We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional…
We derive curvature counterterms in two-dimensional gravity coupled to conformal matter up to infinite order. By construction the higher-order action is equivalent to a finite first-order theory with auxiliary scalar. Due to this…
We review some of our recent results concerning the relationship between the Real-Space Renormalization Group method and Quantum Groups. We show this relation by applying real-space RG methods to study two quantum group invariant…
Perturbative canonical quantum gravity is considered, when coupled to a renormalizable model for matter fields. It is proposed that the functional integral over the dilaton field should be disentangled from the other integrations over the…
A model of matter-coupled gravity in two dimensions is quantized. The crucial requirement for performing the quantization is the vanishing of the conformal anomaly, which is achieved by tuning a parameter in the interaction potential. The…
Recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non-classical modification of the ground state wave function leads to a result that eliminates term-by-term divergences that arise in a…