Related papers: Simplicial Graviton from Selfdual Ashtekar Variabl…
Topological gravity is the reduction of general relativity to flat space-times. A lattice model describing topological gravity is developed starting from a Hamiltonian lattice version of $B\w F$ theory. The extra symmetries not present in…
We consider the coupling of a scalar field to linearised gravity and derive a relativistic gravitationally induced decoherence model using Ashtekar variables. The model is formulated at the gauge invariant level using suitable geometrical…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
We review the classical formulation of general relativity as an SL(2,C) gauge theory in terms of Ashtekar's selfdual variables and reality conditions for the spatial metric (RCI) and its evolution (RCII), and we add some new observations…
The super-Hamiltonian of 4-dimensional gravity as simplified by Ashtekar through the use of gauge potential and densitized triad variables can furthermore be succinctly expressed as a Poisson bracket between the volume element and other…
We describe the canonical phase space of asymptotically flat gravity in Ashtekar-Barbero variables. We show that the Gauss constraint multiplier must fall off slower than previously considered in order to recover ADM phase space. The…
The issue of local gauge invariance in the simplicial lattice formulation of gravity is examined. We exhibit explicitly, both in the weak field expansion about flat space, and subsequently for arbitrarily triangulated background manifolds,…
In Loop Quantum Gravity, tremendous progress has been made using the Ashtekar-Barbero variables. These variables, defined in a gauge-fixing of the theory, correspond to a parametrization of the solutions of the so-called simplicity…
We introduce a reduced model for a real sector of complexified Ashtekar gravity that does not correspond to a subset of Einstein's gravity but for which the programme of canonical quantization can be carried out completely, both, via the…
A key point in the spin foam approach to quantum gravity is the implementation of simplicity constraints in the partition functions of the models. Here, we discuss the imposition of these constraints in a phase space setting corresponding…
The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the…
We develop the general formalism for performing perturbative diagrammatic expansions in the lattice theory of quantum gravity. The results help establish a precise correspondence between continuum and lattice quantities, and should be a…
We solve perturbative constraints and eliminate gauge freedom for Ashtekar's gravity on de Sitter background. We show that the reduced phase space consists of transverse, traceless, symmetric fluctuations of the triad and of transverse,…
We study the gravitational helicity using the covariant phase space method. Starting from the covariant phase space of general relativity expressed in terms of connection variables, we construct the symplectic form and identify a duality…
The Ashtekar formulation of 2+1 gravity differs from the geometrodynamical and Witten descriptions when the 2-metric is degenerate. We study the phase space of 2+1 gravity in the Ashtekar formulation to understand these degenerate solutions…
Using Krasnov's formulation of General Relativity (GR), we develop a lightcone ansatz for self-dual gravity (along with linearized anti-self-dual perturbations) in the Poincare patch of de Sitter space. This amounts to a generalization of…
Unlike scalar and gauge field theories in four dimensions, gravity is not perturbatively renormalizable and as a result perturbation theory is badly divergent. Often the method of choice for investigating nonperturbative effects has been…
We propose a new, discretized model for the study of 3+1-dimensional canonical quantum gravity, based on the classical $SL(2,\C)$-connection formulation. The discretization takes place on a topological $N^3$- lattice with periodic boundary…
We study the degrees of freedom of the metric in a general class of higher derivative gravity models, which are interesting in the context of quantum gravity as they are (super)renormalizable. First, we linearize the theory for a flat…
The lattice formulation of quantum gravity provides a natural framework in which non-perturbative properties of the ground state can be studied in detail. In this paper we investigate how the lattice results relate to the continuum…