Spontaneous compactification —on a R × S background— in 2D induced quantum gravity (considered as a toy model for more fundamental quantum gravity) is analyzed in the gauge-independent effective action formalism. It is shown that such compactification is stable, in contradistinction to multidimensional quantum gravity on a R×S (D > 2) background —which is known to be one-loop unstable. On leave...

The main part of this presentation is a review of the original works [14, 15, 16, 17, 18, 19] on the perturbative approach to the 2-dimensional quantum gravity. We discuss the renormalization of the two-dimensional dilaton gravity in a covariant gauge, the form of the quantum corrections to the classical potential, and the conditions of Weyl invariance in a theory of string coupled to 2d quantu...

LEE SMOLIN, a theoretical physicist, is concerned with quantum gravity,"the name we give to the theory that unifies all the physics now under construction." More specifically, he is a co-inventor of an approach called loop quantum gravity. In 2001, he became a founding member and research physicist of the Perimeter Institute for Theoretical Physics, in Waterloo, Ontario. Smolin is the author of...

I develop a phenomenological approach to the description of the noise levels that the space-time foam of quantum gravity could induce in modern gravity-wave detectors. Various possibilities are considered, including white noise and random-walk noise. In particular, I find that the sensitivity level expected for the planned LIGO and VIRGO interferometers and for the next upgrade of the NAUTILUS ...

An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after reconstructing an algebraic canonical formulation on analytical dynamics. The remarkable fact is that the constraint equation of the gravitational system is algebraical...

Spacetime as we know and love it is lost in most approaches to quantum gravity. For many of these approaches, as inchoate and incomplete as they may be, one of the main challenges is to relate what they take to be the fundamental non-spatiotemporal structure of the world back to the classical spacetime of GR. The present essay investigates how spacetime is lost and how it may be regained in one...

The problem of how space–time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian ...

We address the issue of recovering the time-dependent Schrödinger equation from quantum gravity in a natural way. To reach this aim it is necessary to understand the nonoccurrence of certain superpositions in quantum gravity. We explore various possible explanations and their relation. These are the delocalisation of interference terms through interaction with irrelevant degrees of freedom (dec...

We study quantum gravity in more than four dimensions by means of an exact functional flow. A non-trivial ultraviolet fixed point is found in the Einstein–Hilbert theory. It is shown that our results for the fixed point and universal scaling exponents are stable. If the fixed point persists in extended truncations, quantum gravity in the metric field is asymptotically safe. We indicate physical...

General lectures on quantum gravity. 1 General Questions on Quantum Gravity It is not clear at all what is the problem in quantum gravity (cf. [3] or [8] for general reviews, written in the same spirit as the present one). The answers to the following questions are not known, and I believe it can do no harm to think about them before embarking in a more technical discussion. To begin, it has be...