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.

scholarly journals Status of Background-Independent Coarse Graining in Tensor Models for Quantum Gravity

Universe ◽  
2019 ◽  
Vol 5 (2) ◽  
pp. 53 ◽  
Author(s):  
Astrid Eichhorn ◽  
Tim Koslowski ◽  
Antonio Pereira
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Continuum Limit ◽  
Three Dimensional ◽  
Coarse Graining ◽  
Discrete Models ◽  
Practical Implementation ◽  
Tensor Model ◽  
Independent Form ◽  
Tensor Models

A background-independent route towards a universal continuum limit in discrete models of quantum gravity proceeds through a background-independent form of coarse graining. This review provides a pedagogical introduction to the conceptual ideas underlying the use of the number of degrees of freedom as a scale for a Renormalization Group flow. We focus on tensor models, for which we explain how the tensor size serves as the scale for a background-independent coarse-graining flow. This flow provides a new probe of a universal continuum limit in tensor models. We review the development and setup of this tool and summarize results in the two- and three-dimensional case. Moreover, we provide a step-by-step guide to the practical implementation of these ideas and tools by deriving the flow of couplings in a rank-4-tensor model. We discuss the phenomenon of dimensional reduction in these models and find tentative first hints for an interacting fixed point with potential relevance for the continuum limit in four-dimensional quantum gravity.

PROPERTIES OF LOOP EQUATIONS FOR THE HERMITIAN MATRIX MODEL AND FOR TWO-DIMENSIONAL QUANTUM GRAVITY

1990 ◽  
Vol 05 (22) ◽  
pp. 1753-1763 ◽  
Author(s):  
J. AMBJØRN ◽  
YU. M. MAKEENKO
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
General Procedure ◽  
Iterative Solution ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Continuum Equation ◽  
Hermitian Matrix Model ◽  
The Continuum

We study the properties of the loop equations for the N × N Hermitian matrix model with arbitrary (even) interaction as well as of their continuum limit, associated with the two-dimensional quantum gravity. We apply the general procedure of iterative solution proposed recently by David. We relate the specific heat to the singular behavior of the connected correlator of two loops. We solve the continuum equation to a few lower orders in the string coupling constant, obtaining results for macroscopic loops including the case of a multicritical fixed point.

scholarly journals Langevin Simulation of a Bottomless Hermitian Matrix Model for Two Dimensional Quantum Gravity

1994 ◽  
Vol 91 (3) ◽  
pp. 599-610 ◽  
Author(s):  
M. Kanenaga ◽  
M. Mizutani ◽  
M. Namiki ◽  
I. Ohba ◽  
S. Tanaka
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
Two Dimensional ◽  
Langevin Simulation ◽  
Hermitian Matrix Model

The development of three-dimensional wave-packets in unbounded parallel flows

1968 ◽  
Vol 32 (4) ◽  
pp. 801-808 ◽  
Author(s):  
M. Gaster ◽  
A. Davey
Keyword(s):  
Wave Packet ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Mean Flow ◽  
Physical Plane ◽  
Parallel Flows ◽  
Flow Velocity Profile ◽  
The Stability ◽  
Special Case ◽  
Dimensional Wave

In this paper we examine the stability of a two-dimensional wake profile of the form u(y) = U∞(1 – r e-sy2) with respect to a pulsed disturbance at a point in the fluid. The disturbed flow forms an expanding wave packet which is convected downstream. Far downstream, where asymptotic expansions are valid, the motion at any point in the wave packet is described by a particular three-dimensional wave having complex wave-numbers. In the special case of very unstable flows, where viscosity does not have a significant influence, it is possible to evaluate the three-dimensional eigenvalues in terms of two-dimensional ones using the inviscid form of Squire's transformation. In this way each point in the physical plane can be linked to a particular two-dimensional wave growing in both space and time by simple algebraic expressions which are independent of the mean flow velocity profile. Computed eigenvalues for the wake profile are used in these relations to find the behaviour of the wave packet in the physical plane.

Crystallography of quasi-crystals

1986 ◽  
Vol 42 (4) ◽  
pp. 261-271 ◽  
Author(s):  
T. Janssen
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Crystal Phase ◽  
Two Dimensional ◽  
Space Group ◽  
Quasi Crystals ◽  
Special Case

The symmetry of quasi-crystals, a class of materials that has recently aroused interest, is discussed. It is shown that a quasi-crystal is a special case of an incommensurate crystal phase and that it can be described by a space group in more than three dimensions. A number of relevant three-dimensional quasi-crystals is discussed, in particular dihedral and icosahedral structures. The symmetry considerations are also applied to the two-dimensional Penrose patterns.

scholarly journals Asymptotic Expansion of the Multi-Orientable Random Tensor Model

10.37236/4629 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Eric Fusy ◽  
Adrian Tanasa
Keyword(s):  
Asymptotic Expansion ◽  
Matrix Models ◽  
Three Dimensional ◽  
Natural Generalization ◽  
General Term ◽  
Tensor Model ◽  
Half Integer ◽  
Tensor Models ◽  
Random Tensor

Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the respective graph. In this paper we analyze the general term of the asymptotic expanion in $N$, the size of the tensor, of a particular random tensor model, the multi-orientable tensor model. We perform their enumeration and we establish which are the dominant configurations of a given degree.

scholarly journals Modelling nonlinear hydroelastic waves

2011 ◽  
Vol 369 (1947) ◽  
pp. 2942-2956 ◽  
Author(s):  
P. I. Plotnikov ◽  
J. F. Toland
Keyword(s):  
Wave Speed ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Lagrangian Description ◽  
Two Dimensional ◽  
Cosserat Theory ◽  
Elastic Sheet ◽  
Eulerian Description ◽  
Eulerian Coordinates ◽  
Special Case

This paper uses the special Cosserat theory of hyperelastic shells satisfying Kirchoff’s hypothesis and irrotational flow theory to model the interaction between a heavy thin elastic sheet and an infinite ocean beneath it. From a general discussion of three-dimensional motions, involving an Eulerian description of the flow and a Lagrangian description of the elastic sheet, a special case of two-dimensional travelling waves with two wave speed parameters, one for the sheet and another for the fluid, is developed only in terms of Eulerian coordinates.

MATHEMATICAL ASPECTS OF THE NON-PERTURBATIVE 2D QUANTUM GRAVITY

1990 ◽  
Vol 05 (25) ◽  
pp. 2079-2083 ◽  
Author(s):  
A. R. ITS ◽  
A. V. KITAEV
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
Continuous Limit ◽  
Hermitian Matrix Model

We present rigorous mathematical results for the continuous limit for the hermitian matrix model in connection with the non-perturbative theory of 2D quantum gravity.

scholarly journals THE LOWEST MODES AROUND GAUSSIAN SOLUTIONS OF TENSOR MODELS AND THE GENERAL RELATIVITY

2008 ◽  
Vol 23 (24) ◽  
pp. 3863-3890 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
General Relativity ◽  
Two Dimensions ◽  
Tensor Model ◽  
Momentum Dependence ◽  
Two Dimensional ◽  
Renormalization Procedure ◽  
Metric Tensor ◽  
Tensor Models ◽  
General Coordinate Transformation ◽  
Metric Fluctuations

In the paper arXiv:0706.1618[hep-th], the number distribution of the low-lying spectra around Gaussian solutions representing various dimensional fuzzy tori of a tensor model was numerically shown to be in accordance with the general relativity on tori. In this paper, I perform more detailed numerical analysis of the properties of the modes for two-dimensional fuzzy tori, and obtain conclusive evidences for the agreement. Under a proposed correspondence between the rank-3 tensor in tensor models and the metric tensor in the general relativity, conclusive agreement is obtained between the profiles of the low-lying modes in a tensor model and the metric modes transverse to the general coordinate transformation. Moreover, the low-lying modes are shown to be well on a massless trajectory with quartic momentum dependence in the tensor model. This is in agreement with that the lowest momentum dependence of metric fluctuations in the general relativity will come from the R2-term, since the R-term is topological in two dimensions. These evidences support the idea that the low-lying low-momentum dynamics around the Gaussian solutions of tensor models is described by the general relativity. I also propose a renormalization procedure for tensor models. A classical application of the procedure makes the patterns of the low-lying spectra drastically clearer, and suggests also the existence of massive trajectories.

Gradients of Distortion Seen in the Context of the Ponzo Illusion and Other Contours

1968 ◽  
Vol 20 (2) ◽  
pp. 212-217 ◽  
Author(s):  
Gerald H. Fisher
Keyword(s):  
Three Dimensional ◽  
Angular Size ◽  
Ponzo Illusion ◽  
Two Dimensional ◽  
Spatial Distortion ◽  
Special Case

It is suggested that the spatial distortion evident in the Ponzo figure is a special case of a more general illusion in which a gradient of attenuation appears within areas bounded by angular brackets. The magnitude of this gradient is measured in five lines seen against a number of angular contexts. A similar gradient appears also in the presence of single oblique lines. Accordingly, it is suggested that the distortions seen in the figures usually referred to as “the angle illusions” depend upon the presence of contours which do not necessarily define angles. The implications of these findings for certain existing theories which suggest that some illusions depend upon apparent-distortion of angular size and that they contain features usually associated with two-dimensional perspective projections of typical three-dimensional scenes are discussed.

Sign in / Sign up

Export Citation Format

Share Document