scholarly journals Noncomputability arising in dynamical triangulation model of four-dimensional Quantum Gravity

1993 ◽  
Vol 157 (1) ◽  
pp. 93-98 ◽  
Author(s):  
A. Nabutovsky ◽  
R. Ben-Av
Keyword(s):  
Quantum Gravity ◽  
Dynamical Triangulation

scholarly journals Searching for a continuum limit in causal dynamical triangulation quantum gravity

2016 ◽  
Vol 93 (10) ◽  
Author(s):  
J. Ambjorn ◽  
D. N. Coumbe ◽  
J. Gizbert-Studnicki ◽  
J. Jurkiewicz
Keyword(s):  
Quantum Gravity ◽  
Continuum Limit ◽  
Dynamical Triangulation

scholarly journals A toy model of discretized gravity in two dimensions and its extensions

2017 ◽  
Vol 32 (28) ◽  
pp. 1750149
Author(s):  
Marcello Rotondo ◽  
Shin’ichi Nojiri
Keyword(s):  
Quantum Gravity ◽  
Continuum Limit ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Expectation Value ◽  
Dynamical Triangulation ◽  
Physical Quantities ◽  
Euclidean Signature

We propose a toy model of quantum gravity in two dimensions with Euclidean signature. The model is given by a kind of discretization which is different from the dynamical triangulation. We show that there exists a continuum limit and we can calculate some physical quantities such as the expectation value of the area, that is, the volume of the two-dimensional Euclidean spacetime. We also consider the extensions of the model to higher dimensions.

SIMULATIONS OF FOUR-DIMENSIONAL SIMPLICIAL QUANTUM GRAVITY AS DYNAMICAL TRIANGULATION

1992 ◽  
Vol 07 (12) ◽  
pp. 1039-1061 ◽  
Author(s):  
M.E. AGISHTEIN ◽  
A.A. MIGDAL
Keyword(s):  
Phase Transition ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Order Phase Transition ◽  
Transition Point ◽  
Second Order ◽  
Closed Universe ◽  
Statistical Limit ◽  
Dynamical Triangulation ◽  
Second Order Phase Transition

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 cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: we reached about 5×104 simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model should be further adjusted to reach the second order phase transition point, where the correlation length grows to infinity. We varied the gravitational constant, and we found the first order phase transition, similar to the one found in three-dimensional model, except in 4D the fluctuations are rather large at the transition point, so that this is close to the second order phase transition. The average curvature in cutoff units is large and positive in one phase (gravity), and small negative in another (antigravity). We studied the fractal geometry of both phases, using the heavy particle propagator to define the geodesic map, as well as with the old approach using the shortest lattice paths. The heavy propagator geodesic appeared to be much smoother, so that the scaling laws were found, corresponding to finite fractal dimensions: D+~2.3 in the gravity phase and D−~4.6 in the antigravity phase. Similar, but somewhat lower numbers were obtained from the heat kernel singularity. The influence of the αR2 terms in 2, 3 and 4 dimensions is discussed.

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