Related papers: A Validation of Causal Dynamical Triangulations
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
The Causal Dynamical Triangulation model of quantum gravity (CDT) has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of…
Causal dynamical triangulations allows for a non perturbative approach to quantum gravity. In this article a solution for dimers coupled to CDT is presented and some of the conceptual problems that arise are reflected upon.
Is there an approach to quantum gravity which is conceptually simple, relies on very few fundamental physical principles and ingredients, emphasizes geometric (as opposed to algebraic) properties, comes with a definite numerical…
Causal Dynamical Triangulations is a background independent approach to quantum gravity. We show that there exists an effective transfer matrix labeled by the scale factor which properly describes the evolution of the quantum universe. In…
Borrowing techniques from cosmology, I compute the power spectrum of quantum fluctuations in (2+1)-dimensional causal dynamical triangulations, a promising discrete path integral approach to quantum gravity. The results agree with those of…
We perform a detailed investigation of the phase structure and the semiclassical effective action of (2+1)-dimensional Causal Dynamical Triangulations (CDT) quantum gravity using computer simulations. On the one hand, we study the effect of…
We introduce a new methodology to characterize properties of quantum spacetime in a strongly quantum-fluctuating regime, using tools from topological data analysis. Starting from a microscopic quantum geometry, generated nonperturbatively…
In this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative…
We investigate the impact of spatial topology in 3+1 dimensional causal dynamical triangulations (CDT) by performing numerical simulations with toroidal spatial topology instead of the previously used spherical topology. In the case of…
We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual…
We analyze the universal properties of a new two-dimensional quantum gravity model defined in terms of Locally Causal Dynamical Triangulations (LCDT). Measuring the Hausdorff and spectral dimensions of the dynamical geometrical ensemble, we…
Causal Dynamical Triangulations is a non-perturbative quantum gravity model, defined with a lattice cut-off. The model can be viewed as defined with a proper time but with no reference to any three-dimensional spatial background geometry.…
The aim of the causal dynamical triangulations approach is to define nonperturbatively a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. My aim in this paper is to give a concise yet…
The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological constant. We present the evidence…
The two-dimensional causal dynamical triangulations ($2$d CDT) is a lattice model of quantum geometry. In $2$d CDT, one can deal with the quantum effects analytically and explore the physics through the continuum limit. The continuum theory…
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.
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 show that proper time, when defined in the quantum theory of 2d gravity, becomes identical to the stochastic time associated with the stochastic quantization of space. This observation was first made by Kawai and collaborators in the…
We study the continuum limit of a "radially reduced" approximation of Causal Dynamical Triangulations (CDT), so-called multigraph ensembles, and explain why they serve as realistic toy models to study the dimensional reduction observed in…