arXiv subjects
Publications and source records attributed to Bas V. de Bakker.
In the dynamical triangulation model of four dimensional euclidean quantum gravity we investigate gravitational binding. Two scalar test particles (quenched approximation) have a positive binding energy, thereby showing that the model can represent gravitational attraction.
We confirm recent claims that, contrary to what was generally believed, the phase transition of the dynamical triangulation model of four-dimensional quantum gravity is of first order. We have looked at this at a volume of 64,000 four-simplices, where the evidence in the form of a double peak histogram of the action is quite clear.
This is my PhD thesis on four-dimensional simplicial quantum gravity using the dynamical triangulation model. Most of the results we have published in separate papers are collected here for your convenience. Some new results have been added as well. Besides these results this thesis also contains an introduction to simplicial quantum gravity and a detailed description of my dynamical triangulation program for arbitrary dimension. Some small formal parts are in Dutch.
In the dynamical triangulation model of 4D euclidean quantum gravity we measure two-point functions of the scalar curvature as a function of the geodesic distance. To get the correlations it turns out that we need to subtract a squared one-point function which, although this seems paradoxical, depends on the distance. At the transition and in the elongated phase we observe a power law behaviour, while in the crumpled phase we cannot find a simple function to describe it.
We study the average number of simplices $N'(r)$ at geodesic distance $r$ in the dynamical triangulation model of euclidean quantum gravity in four dimensions. We use $N'(r)$ to explore definitions of curvature and of effective global dimension. An effective curvature $R_V$ goes from negative values for low $κ_2$ (the inverse bare Newton constant) to slightly positive values around the transition $κ_2^c$. Far above the transition $R_V$ is hard to compute. This $R_V$ depends on the distance scale involved and we therefore investigate a similar explicitly $r$ dependent `running' curvature $R_{\rm eff}(r)$. This increases from values of order $R_V$ at intermediate distances to very high values at short distances. A global dimension $d$ goes from high values in the region with low $κ_2$ to $d=2$ at high $κ_2$. At the transition $d$ is consistent with 4. We present evidence for scaling of $N'(r)$ and introduce a scaling dimension $d_s$ which turns out to be approximately 4 in both weak and strong coupling regions. We discuss possible implications of the results, the emergence of classical euclidean spacetime and a possible `triviality' of the theory.
Due to the unrecognizability of certain manifolds there must exist pairs of triangulations of these manifolds that can only be reached from each other by going through an intermediate state that is very large. This might reduce the reliability of dynamical triangulation, because there will be states that will not be reached in practice. We investigate this problem numerically for the manifold $S^5$, which is known to be unrecognizable, but see no sign of these unreachable states.
We consider a dynamical triangulation model of euclidean quantum gravity where the topology is not fixed. This model is equivalent to a tensor generalization of the matrix model of two dimensional quantum gravity. A set of moves is given that allows Monte Carlo simulation of this model. Some preliminary results are presented for the case of four dimensions.
The number of configurations of the dynamical triangulation model of 4D euclidean quantum gravity appears to grow faster than exponentially with the volume, with the implication that the system would end up in the crumpled phase for any fixed $κ_2$ (inverse bare Newton constant). However, a scaling region is not excluded if we allow $κ_2$ to go to infinity together with the volume.