Related papers: An Isometric Dynamics for a Causal Set Approach to…
This paper explores the connection between causality and many-body dynamics by studying the algebraic structure of tri-partite unitaries ('walls') which permanently arrest local operator spreading in their time-periodic evolution. We show…
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…
One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…
We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…
A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal…
We perform quantization of a model in which gravity is coupled to a circular dust shell in 2+1 spacetime dimensions. Canonical analysis shows that momentum space of this model is ADS^2-space, and the global chart for it is provided by the…
In order to construct a quantum theory of gravity, we may have to abandon certain assumptions we were making. In particular, the concept of spacetime as a continuum substratum is questioned. Causal Sets is an attempt to construct a quantum…
Within the causal set approach to quantum gravity, a discrete analog of a spacelike region is a set of unrelated elements, or an antichain. In the continuum approximation of the theory, a moment-of-time hypersurface is well represented by…
In a recent proposal using the group field theory approach, a spatially homogeneous (generally anisotropic) universe is described as a quantum gravity condensate of "atoms of space," which allows the derivation of an effective cosmological…
The spacetime discreteness of causal set theory has enabled the formulation of novel spacetime dynamics. In these so-called "growth" dynamics, a causal set spacetime is generated probabilistically by means of a random walk on certain tree…
Causal Dynamical Triangulations is a background independent approach to quantum gravity. In this paper we introduce a phenomenological transfer matrix model, where at each time step a reduced set of quantum states is used. The states are…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
It is believed that gravity will be explained in the framework of the existing quantum theory when one succeeds in eliminating divergencies at large momenta or small distances (although the phenomenon of gravity has been observed only at…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…
An example of a discrete pregeometry on a microscopic scale is introduced. The model is a directed dyadic acyclic graph. This is the particular case of a causal set. The particles in this model must be self-organized repetitive structures.…
Modified gravity theories can be used for the description of homogeneous and isotropic cosmological models through the corresponding field equations. These can be cast into systems of autonomous differential equations because of their sole…
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
We analyse the canonical quantum dynamics of the isotropic universe, as emerging from the Hamiltonian formulation of a metric f(R) gravity, viewed in the Jordan frame. The canonical method of quantization is performed by solving the…
Non-perturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically dominant and pose an obstacle to obtaining…
The causal set approach to quantum gravity embodies the concepts of causality and discreteness. This article explores some foundational and conceptual issues within causal set theory.