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… 

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

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

The universe from scratch

A fascinating and deep question about nature is what one would see if one could probe space and time at smaller and smaller distances. Already the 19th century founders of modern geometry

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

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 Einstein gravity

We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety program in quantum Einstein gravity. Using the continuum approach based upon the effective average action,

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

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

Constructive Tensor Field Theory: the $${T^4_3}$$T34 Model

We build constructively the simplest tensor field theory which requires some renormalization, namely the rank three tensor theory with quartic interactions and propagator inverse of the Laplacian on

References

SHOWING 1-10 OF 48 REFERENCES

Non-perturbative 3d Lorentzian quantum gravity

TLDR
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

TLDR
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.

Scaling in four-dimensional quantum gravity

Simulations of Four-Dimensional Simplicial Quantum Gravity as Dynamical Triangulation

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

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

Integrable 2D Lorentzian gravity and random walks

Causal evolution of spin networks

Renormalization Group and Quantum Gravity

Scaling behavior of quantum four - geometries