Related papers: Discrete structures in gravity
A short review of scalar curvature invariants in gravity theories is presented. We introduce how these invariants are constructed and discuss the minimal number of invariants required for a given spacetime. We then discuss applications of…
We develop an explicit model of quantum gravity coupled to the matter fields of the Standard Model, based on the 3-group structure and the 3BF action, within the framework of higher gauge theory. The model is constructed by providing a…
We consider the application of the consistent lattice quantum gravity approach we introduced recently to the situation of a Friedmann cosmology and also to Bianchi cosmological models. This allows us to work out in detail the computations…
This Ph.D. thesis pursues two goals: The study of the geometrical structure of two-dimensional quantum gravity and in particular its fractal nature. To address these questions we review the continuum formalism of quantum gravity with…
We discuss effects of loss of coherence in low energy quantum systems caused by or related to gravitation, referred to as gravitational decoherence. These effects, resulting from random metric fluctuations, for instance, promise to be…
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
This thesis investigates low-dimensional models of nonperturbative quantum gravity, with a special focus on Causal Dynamical Triangulations (CDT). We define the so-called curvature profile, a new quantum gravitational observable based on…
Starting from an action for discretized gravity we derive a canonical formalism that exactly reproduces the dynamics and (broken) symmetries of the covariant formalism. For linearized Regge calculus on a flat background -- which exhibits…
Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume…
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…
The quantum cosmology of two-dimensional dilaton-gravity models is investigated. A class of models is mapped onto the constrained oscillator-ghost-oscillator model. A number of exact and approximate solutions to the corresponding…
It is well known that gravity in 2+1 dimensions can be recast as Chern-Simons theory, with the gauge group given by the local isometry group, depending on the metric signature and the cosmological constant. Point particles are added into…
A review is given of some 2-dimensional metrics for which noncommutative versions have been found. They serve partially to illustrate a noncommutative extension of the moving-frame formalism. All of these models suggest that there is an…
Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the…
A model of simplicial quantum gravity in three dimensions(3D) was investigated numerically based on the technique of dynamical triangulation (DT). We are concerned with the genus of surfaces appearing on boundaries (i.e., sections) of a 3D…
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
We describe the geomety of a set of scalar fields coupled to gravity. We consider the formalism of a differential Z_2-graded algebra of $2\times 2$ matrices whose elements are differential forms on space-time. The connection and the…
This essay is a tour around many of the lesser known pregeometric models of physics, as well as the mainstream approaches to quantum gravity, in search of common themes which may provide a glimpse of the final theory which must lie behind…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
One can try to define the theory of quantum gravity as the sum over geometries. In two dimensions the sum over {\it Euclidean} geometries can be performed constructively by the method of {\it dynamical triangulations}. One can define a {\it…