Related papers: A Geometric Renormalisation Group in Discrete Quan…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
The density matrix renormalization group (DMRG) is applied to some one-dimensional reaction-diffusion models in the vicinity of and at their critical point. The stochastic time evolution for these models is given in terms of a non-symmetric…
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional…
In the event symmetric approach to quantum gravity it is assumed that the fundamental laws of physics must be invariant under exchange of any two space-time events. The fact that this symmetry if obviously not observed is attributed to the…
Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of space-time is discrete, typically represented in terms of a graph or…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
Considering the scale dependent effective spacetimes implied by the functional renormalization group in d-dimensional Quantum Einstein Gravity, we discuss the representation of entire evolution histories by means of a single, (d +…
It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line…
We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the…
By means of simple models in a flat spacetime manifold we examine some of the issues that arise when quantizing interacting quantum fields in multi-metric backgrounds. In particular we investigate the maintenance of a causal structure in…
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
We revisit the issue of time in quantum geometrodynamics and suggest a quantization procedure on the space of true dynamic variables. This procedure separates the issue of quantization from enforcing the constraints caused by the general…
In the context of real-space renormalization group methods, we propose a novel scheme for quantum systems defined on a D-dimensional lattice. It is based on a coarse-graining transformation that attempts to reduce the amount of entanglement…
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting,…
It is shown that the presence of multiple time scales at a quantum critical point can lead to a breakdown of the loop expansion for critical exponents, since coefficients in the expansion diverge. Consequently, results obtained from…
Loop Quantum Gravity faces challenges in constructing a well-defined Hamiltonian constraint and understanding the quantum notion of time. In this paper these issues are studied by quantizing the $U(1)^3$ model, a simplified system…