Related papers: A non-perturbative Lorentzian path integral for gr…
The search for a mathematical foundation for the path integral of Euclidean quantum gravity calls for the construction of random geometry on the spacetime manifold. Following developments in physics on the two-dimensional theory, random…
Inspired by previous work in 2+1 dimensional quantum gravity, which found evidence for a discretization of time in the quantum theory, we reexamine the issue for the case of pure Lorentzian gravity with vanishing cosmological constant and…
A model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are…
All global solutions of arbitrary topology of the most general 1+1 dimensional dilaton gravity models are obtained. We show that for a generic model there are globally smooth solutions on any non-compact 2-surface. The solution space is…
We re-examine the nonperturbative curvature properties of two-dimensional Euclidean quantum gravity, obtained as the scaling limit of a path integral over dynamical triangulations of a two-sphere, which lies in the same universality class…
We consider the simplicial state-sum model of Ponzano and Regge as a path integral for quantum gravity in three dimensions. We examine the Lorentzian geometry of a single 3-simplex and of a simplicial manifold, and interpret an asymptotic…
Borrowing techniques from cosmology, I compute the power spectrum of quantum fluctuations in (2+1)-dimensional causal dynamical triangulations, a promising discrete path integral approach to quantum gravity. The results agree with those of…
Quantum mechanical transition amplitudes directly tells the probability of each transition and which one is more favourable. Path-integrals offers a systematic methodology to compute this quantum mechanical process in a consistent manner.…
We show that the Hamiltonian of four-dimensional Lorentzian gravity, defined on a space of real, SU(2)-valued connections, in spite of its non-polynomiality possesses a natural quantum analogue in a lattice-discretized formulation of the…
This article is an overview of the use of so-called Euclidean Dynamical Triangulations (EDT) and Causal Dynamical Triangulations (CDT) as lattice regularizations of quantum gravity. The lattice regularizations have been very successful in…
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate…
It is suggested that not only the curvature, but also the signature of spacetime is subject to quantum fluctuations. A generalized D-dimensional spacetime metric of the form $g_{\mu \nu}=e^a_\mu \eta_{ab} e^b_\nu$ is introduced, where…
In this work a loop quantum corrected model is obtained for spherically symmetric space-times in the vacuum. This effective model is derived by the use of the path integral method, previously employed in several models of Loop Quantum…
I review recent progress in simplicial quantum gravity in three and four dimensions, in particular new results on the phase structure of modified models of dynamical triangulations, the application of a strong-coupling expansion, and the…
Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure…
We analyze simplicial quantum gravity in four dimensions using the Regge approach. The existence of an entropy dominated phase with small negative curvature is investigated in detail. It turns out that observables of the system possess…
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…
We introduce a generalized version of the Causal Dynamical Triangulations (CDT) formulation of quantum gravity, in which the regularized, triangulated path integral histories retain their causal properties, but do not have a preferred…
We propose a new rigorous time-slicing construction of the phase space Path Integrals for propagators both in Quantum Mechanics and Quantum Field Theory for a fairly general class of quantum observables (e.g. the Schroedinger hamiltonians…