scholarly journals Extrinsic curvature in two-dimensional causal dynamical triangulation

2016 ◽  
Vol 94 (6) ◽  
Author(s):  
Lisa Glaser ◽  
Thomas P. Sotiriou ◽  
Silke Weinfurtner
Keyword(s):  
Extrinsic Curvature ◽  
Two Dimensional ◽  
Dynamical Triangulation

scholarly journals ON RELATION BETWEEN GEOMETRIC MOMENTUM AND ANNIHILATION OPERATORS ON A TWO-DIMENSIONAL SPHERE

2013 ◽  
Vol 10 (06) ◽  
pp. 1320007 ◽  
Author(s):  
Q. H. LIU ◽  
Y. SHEN ◽  
D. M. XUN ◽  
X. WANG
Keyword(s):  
Angular Momentum ◽  
Coherent States ◽  
Three Dimensional ◽  
Extrinsic Curvature ◽  
Flat Space ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Intrinsic Geometry

With a recently introduced geometric momentum that depends on the extrinsic curvature and offers a proper description of momentum on two-dimensional sphere, we show that the annihilation operators whose eigenstates are coherent states on the sphere take the expected form αx + iβp, where α and β are two operators that depend on the angular momentum and x and p are the position and the geometric momentum, respectively. Since the geometric momentum is manifestly a consequence of embedding the two-dimensional sphere in the three-dimensional flat space, the coherent states reflects some aspects beyond the intrinsic geometry of the surfaces.

RECURSIVE SAMPLING OF PLANAR GRAPHS AND FRACTAL PROPERTIES OF A TWO-DIMENSIONAL QUANTUM GRAVITY

1990 ◽  
Vol 01 (01) ◽  
pp. 165-179 ◽  
Author(s):  
MICHAEL E. AGISHTEIN ◽  
ALEXANDER A. MIGDAL
Keyword(s):  
Monte Carlo ◽  
Random Graphs ◽  
Planar Graphs ◽  
Two Dimensional ◽  
Cubic Graphs ◽  
New Approach ◽  
Standard Methods ◽  
Fractal Properties ◽  
Dimensional Gravity ◽  
Dynamical Triangulation

We describe a new approach to the Monte-Carlo simulations of two-dimensional gravity. Standard dynamical triangulation technique was combined with results of direct enumeration of the cubic graphs. As a result we were able to build large (128K vertices) statistically independent random graphs directly. The quantitative correspondence between our results and those obtained by standard methods has been observed. The algorithm proved to be so efficient that we were able to conduct all the simulations, which usually require the most powerful computers, on an Iris workstation. An opportunity to generate large random graphs allowed us to observe that the internal geometry of random surfaces is more complicated than simple fractals. External geometry also proved to be rather peculiar.

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.

scholarly journals 2D QUANTUM GRAVITY: THREE STATES OF SURFACES

1998 ◽  
Vol 13 (04) ◽  
pp. 583-605 ◽  
Author(s):  
A. FUJITSU ◽  
N. TSUDA ◽  
T YUKAWA
Keyword(s):  
Two Dimensional ◽  
Dimensional Parameter ◽  
Random Surfaces ◽  
Branched Polymer ◽  
Higher Derivative ◽  
Pure Gravity ◽  
Dynamical Triangulation ◽  
Baby Universes ◽  
Ising Spins ◽  
Baby Universe

Two-dimensional random surfaces are studied numerically by the dynamical triangulation method. In order to generate various kinds of random surfaces, two higher derivative terms are added to the action. The structures of surfaces, two higher derivative terms are added to the action. The structures of surfaces in the two-dimensional parameter space are classified into three states: flat surface, crumpled surface and branched polymer. In addition, there exists a special point (pure gravity) corresponding to the universal fractal surface. A new probe to detect branched polymers is proposed by using the analysis of minimum neck baby universe. This method can clearly distinguish the branched polymer phase from others according to the sizes and arrangements of baby universes. The size and arrangement of baby universes change drastically for each state. The phases of surfaces coupled with multi-Ising spins are studied in a similar manner.

GEOMETRIC CHARACTERIZATION OF STATES IN TWO-DIMENSIONAL QUANTUM GRAVITY

1990 ◽  
Vol 05 (12) ◽  
pp. 965-977 ◽  
Author(s):  
MICHAEL E. AGISHTEIN ◽  
LAURENCE JACOBS ◽  
ALEXANDER A. MIGDAL ◽  
JOHN L. RICHARDSON
Keyword(s):  
Quantum Gravity ◽  
Large Scale ◽  
Geometric Characterization ◽  
Two Dimensional ◽  
Internal Geometry ◽  
Internal Radius ◽  
First Results ◽  
Internal Volume ◽  
Dynamical Triangulation

We report first results of a large-scale simulation of two-dimensional quantum gravity using the dynamical triangulation model for systems of up to sixteen thousand triangles. Our results for the internal geometry show an unexpectedly complicated behavior of the internal volume as function of the internal radius. A simple fractal characterization is inadequate to describe the geometry of the states in the system.

TENSOR MODEL FOR GRAVITY AND ORIENTABILITY OF MANIFOLD

1991 ◽  
Vol 06 (28) ◽  
pp. 2613-2623 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
Quantum Gravity ◽  
Hermitian Matrix ◽  
Three Dimensional ◽  
Tensor Model ◽  
Two Dimensional ◽  
Tensor Models ◽  
Arbitrary Dimensions ◽  
Dynamical Triangulation ◽  
Hermitian Matrix Model ◽  
Special Case

We investigate the relation between rank-three tensor models and the dynamical triangulation model of three-dimensional quantum gravity, and discuss the orientability of the manifold and the corresponding tensor models. We generalize the orientable tensor models to arbitrary dimensions, which include the two-dimensional Hermitian matrix model as a special case.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

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