# Simplicial Euclidean and Lorentzian Quantum Gravity

@article{Ambjorn2002SimplicialEA,
title={Simplicial Euclidean and Lorentzian Quantum Gravity},
author={Jan Ambjorn},
journal={arXiv: General Relativity and Quantum Cosmology},
year={2002}
}
• J. Ambjorn
• Published 9 January 2002
• Mathematics
• arXiv: General Relativity and Quantum Cosmology
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 proper-time} propagator. This propagator can be used to calculate generalized Hartle-Hawking amplitudes and it can be used to understand the the fractal structure of {\it quantum geometry}. In higher dimensions the philosophy of defining the quantum theory…
29 Citations

## Figures from this paper

A discrete history of the Lorentzian path integral
In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a
Fractal spacetime structure in asymptotically safe gravity
• Physics
• 2005
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-planckian distances it predicts that
On the renormalization of truncated quantum Einstein gravity
The perturbative renormalizability of the 2-Killing vector reduction of general relativity is investigated. Although non-renormalizable in the standard sense, we show that to all orders of the loop
• Physics
• 2019
Non-commutative geometry today is a new but mature branch of mathematics shedding light on many other areas from number theory to operator algebras. In the 2018 meeting two of these connections were
Spin Foam Models for Quantum Gravity
In this topical review, we review the present status of the spin foam formulation of non-perturbative (background-independent) quantum gravity. The topical review is divided into two parts. In the
Renormalization and asymptotic safety in truncated quantum Einstein gravity
A perturbative quantum theory of the 2-Killing vector reduction of general relativity is constructed. Although non-renormalizable in the standard sense, we show that to all orders of the loop
A hexagon model for 3-d Lorentzian quantum cosmology
• Physics
• 2002
We formulate a dynamically triangulated model of three-dimensional Lorentzian quantum gravity whose spatial sections are flat two tori. It is shown that the combinatorics involved in evaluating the
Random Tensors and Quantum Gravity
We provide an informal introduction to tensor field theories and to their as- sociated renormalization group. We focus more on the general motivations coming from quantum gravity than on the
Quantum Gravity models - brief conceptual summary
After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical continuous
A Renormalizable SYK-Type Tensor Field Theory
• Physics
Annales Henri Poincaré
• 2018
In this paper we introduce a simple field theoretic version of the Carrozza–Tanasa–Klebanov–Tarnopolsky (CTKT) “uncolored” holographic tensor model. It gives a more familiar interpretation to the

## References

SHOWING 1-10 OF 68 REFERENCES
Non-perturbative 3d Lorentzian quantum gravity
• Physics
• 2001
The phase structure of the Wick-rotated path integral in three dimensions with the aid of computer simulations is investigated, finding a whole range of the gravitational coupling constant k{sub 0} for which the functional integral is dominated by nondegenerate three-dimensional space-times.
Crossing the c=1 barrier in 2d Lorentzian quantum gravity
• Physics
• 1999
Analysis of a system of eight Ising models coupled to dynamically triangulated Lorentzian geometries provides evidence for the conjecture that the KPZ values of the critical exponents in 2d Euclidean quantum gravity are entirely due to the presence of baby universes.
Simulations of Four-Dimensional Simplicial Quantum Gravity as Dynamical Triangulation
• Physics
• 1992
Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. We studied simplicial manifolds of spherical topology and found the critical line for the
Quantum geometry with intrinsic local causality
• Physics, Mathematics
• 1998
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by