Related papers: Endeavours in Discrete Lorentzian Geometry; A thes…
We study numerically the dynamical triangulation formulation of two-dimensional quantum gravity using a restricted class of triangulation, so-called minimal triangulations, in which only vertices of coordination number 5, 6, and 7 are…
If the diffeomorphism symmetry of general relativity is fully implemented into a path integral quantum theory, the path integral leads to a partition function which is an invariant of smooth manifolds. We comment on the physical…
We review some recent results from the causal dynamical triangulation (CDT) approach to quantum gravity. We review recent observations of dimensional reduction at a number of previously undetermined points in the parameter space of CDT, and…
We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory…
We propose a computation of curvature of arbitrary two-dimensional surfaces of three-dimensional objects, which is a contribution to discrete gravity with potential applications in network geometry. We begin by linking each point of the…
Several classes of directed acyclic graphs have been investigated in the last two decades, in the context of the Causal Set Program, in search for good discrete models of spacetime. We introduce some statistical indicators that can be used…
We argue that theories of quantum gravity constructed with the help of (Causal) Dynamical Triangulations have given us the most informative, quantitative models to date of quantum spacetime. Most importantly, these are derived dynamically…
We apply the ``consistent discretization'' technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well defined canonical theory that is free of constraints and…
I present aspects of causal set theory (a research programme in quantum gravity) as being en route to achieving a reduction of Lorentzian geometry to causal sets. I take reduction in philosophers' sense; and I argue that the prospects are…
We present a self-contained analysis of theories of discrete 2D gravity coupled to matter, using geometric methods to derive equations for generating functions in terms of free (noncommuting) variables. For the class of discrete gravity…
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal…
We investigate two-dimensional higher derivative gravitational theories in a Riemann-Cartan framework and obtain the most general static black hole solutions in conformal coordinates. We also consider the hamiltonian formulation of the…
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The…
We perform a rigorous piecewise-flat discretization of classical general relativity in the first-order formulation, in both 2+1 and 3+1 dimensions, carefully keeping track of curvature and torsion via holonomies. We show that the resulting…
In the approach of Causal Dynamical Triangulations (CDT), quantum gravity is obtained as a scaling limit of a non-perturbative path integral over space-times whose causal structure plays a crucial role in the construction. After some…
We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space…
In this paper, Dirac Quantization of $3D$ gravity in the first-order formalism is attempted where instead of quantizing the connection and triad fields, the connection and the triad 1-forms themselves are quantized. The exterior derivative…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…
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…
A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of…