Related papers: New action for simplicial gravity in four dimensio…
Spinor gravity is a functional integral formulation of gravity based only on fundamental spinor fields. The vielbein and metric arise as composite objects. Due to the lack of local Lorentz-symmetry new invariants in the effective…
We study 4d simplicial quantum gravity in the dynamical triangulation approach with a non-trivial class of measures. We find that the measure contribution plays an important role, influencing the phase diagram and the nature of the…
This is my PhD thesis on four-dimensional simplicial quantum gravity using the dynamical triangulation model. Most of the results we have published in separate papers are collected here for your convenience. Some new results have been added…
I present a model of discrete gravity, which is formulated in terms of a topological gauge theory with defects. The theory has no local degrees of freedom and the gravitational field is trivial everywhere except at a number of colliding…
This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting…
A crucial property of Weyl gravity is its conformal invariance. It is shown how this gauge symmetry is exactly reflected by the two constraints in the Hamiltonian framework. Since the spatial 3-metric is one of the configuration variables,…
We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the…
We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental…
We demonstrate how some problems arising in simplicial quantum gravity can be successfully addressed within the framework of combinatorial group theory. In particular, we argue that the number of simplicial 3-manifolds having a fixed…
Loop Quantum Gravity heavily relies on a connection formulation of General Relativity such that 1. the connection Poisson commutes with itself and 2. the corresponding gauge group is compact. This can be achieved starting from the Palatini…
This article presents a derivation of the Ponzano--Regge model from a one-dimensional spinor action. The construction starts from the first-order Palatini formalism in three dimensions. We then introduce a simplicial decomposition of the…
Starting from a topological gauge theory in two dimensions with symmetry groups $ISO(2,1)$, $SO(2,1)$ and $SO(1,2)$ we construct a model for gravity with non-trivial coupling to matter. We discuss the equations of motion which are connected…
Loop Quantum Gravity is now a well established approach to quantum gravity. One of the main challenges still faced by the theory is constructing a consistent dynamics which would lead back to the standard dynamics of the gravitational field…
Recently an alternate technique for numerical quantum gravity, dynamical triangulation, has been developed. In this method, the geometry is varied by adding and subtracting equilateral simplices from the simplicial complex. This method…
Scaling relations in four-dimensional simplicial quantum gravity are proposed using the concept of the geodesic distance. Based on the analogy of a loop length distribution in the two-dimensional case, the scaling relations of the boundary…
We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the…
The attempt of extending to higher dimensions the matrix model formulation of two-dimensional quantum gravity leads to the consideration of higher rank tensor models. We discuss how these models relate to four dimensional quantum gravity…
Discrete approaches to gravity, both classical and quantum, are reviewed briefly, with emphasis on the method using piecewise-linear spaces. Models of 3-dimensional quantum gravity involving 6j-symbols are then described, and progress in…
A new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and…
Some results of author's work in a non-geometrical approach to quantum gravity are reviewed here, among them: a quantum mechanism of classical gravity giving a possibility to compute the Newton constant; asymptotic freedom at short…