Related papers: A Geometric Renormalisation Group in Discrete Quan…
Planck-scale physics challenges the classical smooth-spacetime picture by introducing quantum fluctuations that imply a nontrivial spacetime microstructure. We present a framework that encodes these fluctuations by promoting local scale…
Homogeneous and isotropic cosmologies of the Planck era before the classical Einstein equations become valid are studied taking quantum gravitational effects into account. The cosmological evolution equations are renormalization group…
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…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face is to find the discrete protoforms of…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
In the following we undertake to describe how macroscopic space-time (or rather, a microscopic protoform of it) is supposed to emerge as a superstructure of a web of lumps in a stochastic discrete network structure. As in preceding work…
We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse-field Ising model, which is a prototype of random quantum magnets. With this…
We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies…
Quantum entanglement entropy has a geometric character. This is illustrated by the interpretation of Rindler space or black hole entropy as entanglement entropy. In general, one can define a "geometric entropy", associated with an event…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
The density matrix renormalization group (DMRG) has been extended to study quantum phase transitions on random graphs of fixed connectivity. As a relevant example, we have analysed the random Ising model in a transverse field. If the…
In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…
I show that an application of renormalization group arguments may lead to significant corrections to the vacuum decay rate for phase transitions in flat and curved space-time. It can also give some information regarding its dependence on…
Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…
The following is a short report about recent work on discrete physics/mathematics on the Planckscale and the use of the concept of ''random graphs'' in this business, appearing in the group21-proceedings (Gosslar 1996)
The Renormalization Group encodes three concepts that could be key to accelerate progress in quantum gravity. First, it provides a micro-macro connection that could connect microscopic spacetime physics to phenomenology at observationally…
It is well known that the renormalization group equations depend on the scale where they are applied. This phenomenon is especially relevant for the massive fields in curved space, because the decoupling effects may be responsible for…
In various areas of modern physics and in particular in quantum gravity or foundational space-time physics it is of great importance to be in the possession of a systematic procedure by which a macroscopic or continuum limit can be…
An enquiry into the physical nature of time and space and into the ontology of quantum mechanics from a metageometric perspective, resulting from the belief that geometric thought and language are powerless to farther understanding of these…