Quantum fluctuations of the metric, three-geometries and conformal embeddings in four-manifolds

2021 ◽  
Author(s):  
Simon Davis
Keyword(s):  
Path Integrals ◽  
Invariance Group ◽  
Two Dimensional ◽  
Four Dimensions ◽  
Physical Conditions ◽  
Exponential Expansion ◽  
Cotangent Bundles ◽  
Four Manifolds ◽  
Conformal Embeddings ◽  
Natural Relation

In this paper, connections between the path integrals for four-dimensional quantum gravity and string theory are emphasized. It is shown that there is a natural relation between these two path integrals based on the theorems on embeddings of two-dimensional surfaces in four dimensions and four-dimensional manifolds in ten dimensions. The isometry groups of the three-geometries that are spatial hypersurfaces confomally embedded in the four-manifolds are required to be subgroups of [Formula: see text], which is the invariance group of the Pfaffian differential system satisfied by one form in the cotangent bundles on the four-manifolds. Based on this and other physical conditions, the three-geometries are restricted to be [Formula: see text], [Formula: see text] and [Formula: see text] with a boundary, which may be included in the quantum gravitational path integral over four-manifolds which are closed at initial times followed by an exponential expansion compatible with supersymmetry.

The Two-Dimensional CCSMM

2021 ◽  
pp. 32-54
Keyword(s):  
Cyber Security ◽  
Phase 1 ◽  
Maturity Model ◽  
Two Dimensional ◽  
Four Dimensions ◽  
Level 1 ◽  
Level 2

The community cyber security maturity model (CCSMM) defines four dimensions and five implementation mechanisms in describing the relative maturity of an organization or an SLTT's cybersecurity program. These are used in defining levels of maturity and the cybersecurity characteristics of an organization or SLTT at each level. In order to progress from one level to the next, a variety of activities should take place, and these are defined in terms of five different mechanisms. In between two levels are a variety of activities that should take place to help the entity to advance from one level to the next. These groups of activities describe four phases, each of which takes place between two levels. Thus, Phase 1 defines the activities that should occur for an entity to advance from Level 1 to Level 2.

scholarly journals Isotropic Lifshitz scaling in four dimensions

2020 ◽  
Vol 17 (04) ◽  
pp. 2050053 ◽  
Author(s):  
Dario Zappalà
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Critical Dimension ◽  
Two Dimensional ◽  
Continuous Line ◽  
Scalar Theory ◽  
Functional Renormalization Group ◽  
Four Dimensions ◽  
Dimension Formula

The presence of isotropic Lifshitz points for a [Formula: see text]-symmetric scalar theory is investigated with the help of the Functional Renormalization Group. In particular, at the supposed lower critical dimension [Formula: see text], evidence for a continuous line of fixed points is found for the [Formula: see text] theory, and the observed structure presents clear similarities with the properties observed in the two-dimensional Berezinskii–Kosterlitz–Thouless phase.

scholarly journals Recognition of Emotion According to the Physical Elements of the Video

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 649 ◽  
Author(s):  
Jing Zhang ◽  
Xingyu Wen ◽  
Mincheol Whang
Keyword(s):  
Video Production ◽  
Support Vector ◽  
Two Dimensional ◽  
K Nearest Neighbors ◽  
Four Dimensions ◽  
Emotion Elicitation ◽  
Neural Processes ◽  
Physical Elements ◽  
The Impact ◽  
The Relationship

The increasing interest in the effects of emotion on cognitive, social, and neural processes creates a constant need for efficient and reliable techniques for emotion elicitation. Emotions are important in many areas, especially in advertising design and video production. The impact of emotions on the audience plays an important role. This paper analyzes the physical elements in a two-dimensional emotion map by extracting the physical elements of a video (color, light intensity, sound, etc.). We used k-nearest neighbors (K-NN), support vector machine (SVM), and multilayer perceptron (MLP) classifiers in the machine learning method to accurately predict the four dimensions that express emotions, as well as summarize the relationship between the two-dimensional emotion space and physical elements when designing and producing video.

Compacted dimensions and singular plasmonic surfaces

Science ◽  
2017 ◽  
Vol 358 (6365) ◽  
pp. 915-917 ◽  
Author(s):  
J. B. Pendry ◽  
Paloma Arroyo Huidobro ◽  
Yu Luo ◽  
Emanuele Galiffi
Keyword(s):  
Field Theory ◽  
Simple Model ◽  
Surface Plasmon ◽  
Graphene Layer ◽  
Field Theories ◽  
Two Dimensional ◽  
Experimental Realization ◽  
Four Dimensions ◽  
Metal Grating ◽  
Doped Graphene

In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer.

scholarly journals Studies on Polyakov and Nambu–Goto random surface path integrals on QCD(SU(∞)): Interquark potential and phenomenological scattering amplitudes

2017 ◽  
Vol 32 (05) ◽  
pp. 1750030
Author(s):  
Luiz C. L. botelho
Keyword(s):  
Asymptotic Behavior ◽  
Scattering Amplitudes ◽  
Path Integral ◽  
Fourth Order ◽  
Path Integrals ◽  
Infrared Region ◽  
Two Dimensional ◽  
Long Distance ◽  
Random Surface ◽  
Interquark Potential

We present new path integral studies on the Polyakov noncritical and Nambu–Goto critical string theories and their applications to [Formula: see text] interquark potential. We also evaluate the long distance asymptotic behavior of the interquark potential on the Nambu–Goto string theory with an extrinsic term in Polyakov’s string at [Formula: see text]. We also propose an alternative and a new view to covariant Polyakov’s string path integral with a fourth-order two-dimensional quantum gravity, is an effective stringy description for [Formula: see text] at the deep infrared region.

BOSONIC PATH INTEGRALS FOR FOUR-DIMENSIONAL DIRAC PARTICLES

1989 ◽  
Vol 04 (14) ◽  
pp. 3615-3628 ◽  
Author(s):  
PETER ORLAND
Keyword(s):  
Coherent State ◽  
Path Integrals ◽  
Functional Integral ◽  
Three Dimensions ◽  
Four Dimensions ◽  
Dirac Particles ◽  
Relativistic Spin ◽  
State Path

After reviewing coherent state path integrals for nonrelativistic spin in four dimensions (or equivalently, relativistic spin in three dimensions), the Dirac propagator in four dimensions is recast as a functional integral of an (S3×S3)/S1 field. Chiral transformations correspond to a global rotation of this field.

scholarly journals Black hole induced false vacuum decay from first principles

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Andrey Shkerin ◽  
Sergey Sibiryakov
Keyword(s):  
Black Hole ◽  
Decay Rate ◽  
First Principles ◽  
Two Dimensional ◽  
False Vacuum ◽  
Dimensional Model ◽  
Vacuum Decay ◽  
Four Dimensions ◽  
Dilaton Black Hole ◽  
Black Hole Temperature

Abstract We provide a method to calculate the rate of false vacuum decay induced by a black hole. The method uses complex tunneling solutions and consistently takes into account the structure of different quantum vacua in the black hole metric via boundary conditions. The latter are connected to the asymptotic behavior of the time-ordered Green’s function in the corresponding vacua. We illustrate the technique on a two-dimensional toy model of a scalar field with inverted Liouville potential in an external background of a dilaton black hole. We analytically derive the exponential suppression of tunneling from the Boulware, Hartle-Hawking and Unruh vacua and show that they are parametrically different. The Unruh vacuum decay rate is exponentially smaller than the decay rate of the Hartle-Hawking state, though both rates become unsuppressed at high enough black hole temperature. We interpret the vanishing suppression of the Unruh vacuum decay at high temperature as an artifact of the two-dimensional model and discuss why this result can be modified in the realistic case of black holes in four dimensions.

Anomalies in finite amplitudes: Two-dimensional single and triple axial-vector triangles

2018 ◽  
Vol 33 (23) ◽  
pp. 1850136
Author(s):  
O. A. Battistel ◽  
F. Traboussy ◽  
G. Dallabona
Keyword(s):  
Field Theory ◽  
Axial Vector ◽  
Space Time ◽  
Point Of View ◽  
Quantum Field ◽  
Two Dimensional ◽  
Point Function ◽  
Four Dimensions ◽  
Clear Point ◽  
A Chain

An explicit and detailed investigation about the two-dimensional (2D) single and triple axial-vector triangles is presented. Such amplitudes are related to the 2D axial-vector two-point function (AV) through contractions with the external momenta. Given this fact, before considering the triangles, we give a clear point of view for the AV anomalous amplitude. Such point of view is constructed within the context of an alternative strategy to handle the divergences typical of the perturbative solutions of quantum field theory. In the referred procedure all amplitudes in all theories, formulated in odd and even space–time dimensions, renormalizable or not, are treated on the same footing. After performing, in a very detailed way, all the calculations, we conclude that the same phenomenon occurring in the AV amplitude is present also in the finite single and triple axial-vector triangles. The conclusion gives support to the thesis that the phenomenon is present in pseudo-amplitudes belonging to a chain where the divergent AV one is only the simplest structure. It is expected that the same must occur in all even space–time dimensions. In particular, in four dimensions, the single and triple axial box amplitudes must exhibit anomalies too.

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