Related papers: Fractal properties of quantum spacetime
In these lectures we review our present understanding of the fractal structure of two-dimensional Euclidean quantum gravity coupled to matter.
Scaling properties inherent in quantum dynamics have been studied for various systems in terms of acceleration, deceleration and time reversing. We show a scaling property of quantum dynamics on curved space-time where gravity plays an…
We construct matter field theories in ``theory space'' that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and…
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…
In this paper we first show that the usual three dimensionality of space, which is taken for granted, results from the spinorial behaviour of Fermions, which constitute the material content of the universe. It is shown that the resulting…
Hints from a number of different approaches to quantum gravity point to a phenomenon of "spontaneous dimensional reduction" to two spacetime dimensions near the Planck scale. I examine the physical meaning of the term "dimension" in this…
We consider a quantum field theory on a spherically symmetric quantum space time described by loop quantum gravity. The spin network description of space time in such a theory leads to equations for the quantum field that are discrete. We…
For a large region of parameter space involving the cosmological constant and mass parameters, we discuss fluctuating spacetime solutions that are effectively Minkowskian on large time and distance scales. Rapid, small amplitude…
Quantum scale symmetry is the realization of scale invariance in a quantum field theory. No parameters with dimension of length or mass are present in the quantum effective action. Quantum scale symmetry is generated by quantum fluctuations…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
The relevance of the Planck scale to a theory of quantum gravity has become a worryingly little examined assumption that goes unchallenged in the majority of research in this area. However, in all scientific honesty, the significance of…
We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…
The phenomenologically observed flatness - or near flatness - of spacetime cannot be understood as emerging from continuum Planck (or sub-Planck) scales using known physics. Using dimensional arguments it is demonstrated that any…
It has been shown that if one solves self-consistently the semiclassical Einstein equations in the presence of a quantum scalar field, with a cutoff on the number of modes, spacetime become flatter when the cutoff increases. Here we extend…
The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static…
Postulates which lead to Minkowski spacetime are amended in a subtle way, and used to construct a consistent flat spacetime geometry with intrinsic quantum character. Events in the new quantum geometry are described by labels of the form…
We discuss the generic phenomenology of quantum gravity and, in particular, argue that the observable effects of quantum gravity, associated with new, extended, non-local, non-particle-like quanta, and accompanied by a dynamical…
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…
In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker (FLRW) space-times arise as well-defined approximations to specific \emph{quantum} geometries. We initiate the development of a quantum theory of test scalar fields on these…
Simple arguments based on the general properties of quantum fluctuations have been recently shown to imply that quantum fluctuations of spacetime obey the same scaling laws of the velocity fluctuations in a homogeneous incompressible…