Related papers: Quantum gravity on a torus
A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated…
Detailed applications of minisuperspace methods are presented and compared with results obtained in recent years by means of causal dynamical triangulations (CDTs), mainly in the form of effective actions. The analysis sheds light on…
I investigate a discrete model of quantum gravity on a causal null-lattice with \SLC structure group. The description is geometric and foliates in a causal and physically transparent manner. The general observables of this model are…
This work revisits the Euclidean Dynamical Triangulation (DT) approach to non-perturbative quantum gravity in three dimensions. Inspired by a recent combinatorial study by T. Budd and L. Lionni of a subclass of 3-sphere triangulations…
In recent years several approaches to quantum gravity have found evidence for a scale dependent spectral dimension of space-time varying from four at large scales to two at small scales of order of the Planck length. The first evidence came…
Two-dimensional Causal Dynamical Triangulations provides a definition of the path integral for projectable two-dimensional Horava-Lifshitz quantum gravity. We solve the theory coupled to gauge fields.
The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of…
The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
The dynamical generation of a four-dimensional classical universe from nothing but fundamental quantum excitations at the Planck scale is a long-standing challenge to theoretical physicists. A candidate theory of quantum gravity which…
We investigate the geometry of a quantum universe with the topology of the four-torus. The study of non-contractible geodesic loops reveals that a typical quantum geometry consists of a small semi-classical toroidal bulk part, dressed with…
Quantum fields are investigated in the (2+1)-open-universes with non-trivial topologies by the method of images. The universes are locally de Sitter spacetime and anti-de Sitter spacetime. In the present article we study spacetimes whose…
We study the phase diagram of a one-dimensional balls-in-boxes (BIB) model that has been proposed as an effective model for the spatial-volume dynamics of (2+1)-dimensional causal dynamical triangulations (CDT). The latter is a statistical…
Previous work on applications of Abstract Differential Geometry (ADG) to discrete Lorentzian quantum gravity is brought to its categorical climax by organizing the curved finitary spacetime sheaves of quantum causal sets involved therein,…
A lattice regularization for the $2$d projectable Horava-Lifshitz (HL) quantum gravity is known to be the $2$d causal dynamical triangulations (CDT), and the $2$d CDT can be generalized so as to include all possible genus contributions…
To solve the path integral for quantum gravity, one needs to regularise the space-times that are summed over. This regularisation usually is a discretisation, which makes it necessary to give up some paradigms or symmetries of continuum…
We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to…
We formulate the string field theory in zero-dimensional target space corresponding to the two-dimensional quantum gravity theory defined through Causal Dynamical Triangulations. This third quantization of the quantum gravity theory allows…
A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum…
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme--in concert with finite size scaling…