arXiv subjects
Publications and source records attributed to W. Beirl.
We compare different models of a quantum theory of four-dimensional lattice gravity based on Regge's original proposal. From Monte Carlo simulations we calculate two-point functions between geometrical quantities and estimate the masses of the corresponding interaction particles.
We analyze Regge quantum gravity coupled to SU(2) gauge theory on $4^3\times 2$, $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. It turns out that the window of the well-defined phase of the gravity sector where geometrical expectation values are stable extends to negative gravitational couplings as well as to gauge couplings across the deconfinement phase transition. We study the string tension from Polyakov loops, compare with the $β$-function of pure gauge theory and conclude that a physical limit through scaling is possible.
We suggest a generalization of the dynamical triangulation approach to quantum gravity with both timelike and spacelike edges, which can serve as a toy model for quantum gravity in the Lorentz sector in two dimensions. It is possible to consider the model in a purely Lorentzian sector or to relax this constraint and allow local signature changing moves. We show that, with suitable conventions, the model is equivalent to an Ising model coupled to 2D Euclidean quantum gravity and conduct a preliminary numerical simulation of the Lorentz sector.
We examine the phase structure of pure Regge gravity in four dimensions and compare our Monte Carlo results with $Z_2$-link Regge-theory as well as with another formulation of lattice gravity derived from group theoretical considerations. Within all three models we find an extension of the well-defined phase to negative gravitational coupling and a new phase transition. In contrast to the well-known transition at positive coupling there is evidence for a continuous phase transition which might be essential for a possible continuum limit.
We present potentials between static charges from simulations of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. The action consists of the gravitational term given by Regge's discrete version of the Euclidean Einstein action and a gauge term given by the Wilson action, with coupling constants $m_{p}^{2}$ and $β$ respectively. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance $R$. We compare potentials on a flat simplicial lattice with those on a fluctuating Regge skeleton. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations considerably. In two dimensions equivalence to an Ising model with ternary couplings is recovered. First simulations in four dimensions indicate strong similarities to the phase structure of original Regge theory.
We present investigations of the potential between static charges from a simulation of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance $R$. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.
We analyze simplicial quantum gravity in four dimensions using the Regge approach. The existence of an entropy dominated phase with small negative curvature is investigated in detail. It turns out that observables of the system possess finite expectation values although the Einstein-Hilbert action is unbounded. This well-defined phase is found to be stable for a one-parameter family of measures. A preliminary study indicates that the influence of the lattice size on the average curvature is small. We compare our results with those obtained by dynamical triangulation and find qualitative correspondence.
We investigate the interaction mechanism of pure quantum gravity in Regge discretization. We compute volume-volume and link-link correlation functions. In a preliminary analysis the forces turn out to be of Yukawa type, at least on our finite lattice being away from the continuum limit.
Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin system with higher couplings on a Kagome lattice. Various measures acting as external field are considered. Extensions to matter fields and higher dimensions are discussed.
We study quantum gravity in the path-integral formulation using the Regge calculus. In spite of the unbounded gravitational action the existence of an entropy-dominated phase is confirmed. The influence of various types of measures on this phase structure is investigated and our results are compared with those obtained by dynamical triangulation.
We investigate quantum gravity on simplicial lattices using Regge calculus with special emphasize on the problem of the unbounded action. The role of the entropy for the path integral is discussed in detail. Our numerical results show further evidence for the existence of an entropy dominated region with well defined expectation values even for unbounded action. Analyses are performed both for the standard regular triangulation of the 4-torus and for irregularly triangulated lattices obtained by insertion of vertices using barycentric subdivision.
Euclidean quantum-gravity path-integrals are investigated within Regge calculus by computer simulations. The domain of integration is restricted by introducing a lower limit for the fatness of each simplex. We use the standard hypercubic triangulation of the 4-torus and irregularly triangulated lattices obtained by inserting a small number of vertices using barycentric subdivision. For limited fatness we find an entropy dominated phase with small negative curvature both for the regular and the irregular triangulation.
We investigate the influence of the measure in the path integral for Euclidean quantum gravity in four dimensions within the Regge calculus. The action is bounded without additional terms by fixing the average lattice spacing. We set the length scale by a parameter $β$ and consider a scale invariant and a uniform measure. In the low $β$ region we observe a phase with negative curvature and a homogeneous distribution of the link lengths independent of the measure. The large $β$ region is characterized by inhomogeneous link lengths distributions with spikes and positive curvature depending on the measure.