相关论文: More on the exponential bound of four dimensional …
Dynamical triangulations of four-dimensional Euclidean quantum gravity give rise to an interesting, numerically accessible model of quantum gravity. We give a simple introduction to the model and discuss two particularly important issues.…
Simplicial quantum gravity has been proposed as a regularization for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the 4-sphere. The model is well-defined…
We have studied a model which has been proposed as a regularisation for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the four sphere. Using numerical…
It is proven that the partition function of 3-dimensional simplicial gravity has an exponential upper bound with the following assumption: any three dimensional sphere $S^3$ is constructed by repeated identification of neighboring links and…
We present numerical results supporting the existence of an exponential bound in the dynamical triangulation model of three-dimensional quantum gravity.Both the critical coupling and various other quantities show a slow power law approach…
We present the results of a high statistics Monte Carlo study of a model for four dimensional euclidean quantum gravity based on summing over triangulations. We show evidence for two phases; in one there is a logarithmic scaling on the mean…
Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields (N_X) and gauge fields (N_A) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent gamma^{(4)} is…
We show that deciding simulation equivalence and simulation preorder have quadratic lower bounds assuming that the Strong Exponential Time Hypothesis holds. This is in line with the best know quadratic upper bounds of simulation…
A thorough numerical examination for the field theory of 4D quantum gravity (QG) with a special emphasis on the conformal mode dependence has been studied. More clearly than before, we obtain the string susceptibility exponent of the…
Sign problem in fermion quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average sign in QMC simulation approaches…
These Lecture Notes provide an elementary introduction to the quantization of two-dimensional quantum gravity. Nothing beyond undergratuate physics and mathematic is required. Explicit formulas for the partition functions for universes with…
We derive rigorous bounds on corrections to Einstein gravity using unitarity and analyticity of graviton scattering amplitudes. In $D\geq 4$ spacetime dimensions, these consistency conditions mandate positive coefficients for certain…
Two-dimensional quantum gravity with an $R^2$ term is investigated in the continuum framework. It is shown that the partition function for small area $A$ is highly suppressed by an exponential factor $exp \{ -2\pi (1-h)^2/(m^2A) \}$, where…
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
We describe a Monte Carlo procedure for the simulation of dynamically triangulate random surfaces with a boundary (topology of a disk). The algorithm keeps the total number of triangles fixed, while the length of the boundary is allowed to…
A theory of exponential modified gravity which explains both early-time inflation and late-time acceleration, in a unified way, is proposed. The theory successfully passes the local tests and fulfills the cosmological bounds and,…
We extend simulations of simplicial gravity in four dimensions to include {\it degenerate} triangulations and demonstrate that using this ensemble the geometric finite-size effects are much reduced. We provide strong numerical evidence for…
Four principles are proposed to underlie the quantum theory of gravity. We show that these suffice to recover the Einstein equations. We also suggest that MOND results from a modification of the classical equivalence principle, due to…
We determine bounds on the curvature of local patches of spacetime from the requirement of intact long-range chiral symmetry. The bounds arise from a scale-dependent analysis of gravitational catalysis and its influence on the effective…
In canonical quantum gravity, when space is a compact manifold with boundary there is a Hamiltonian given by an integral over the boundary. Here we compute the action of this `boundary Hamiltonian' on observables corresponding to open…