scholarly journals EXTENDED CONFORMAL GROUP AND DSR VELOCITIES ON THE PHYSICAL SURFACE

2006 ◽  
Vol 21 (13n14) ◽  
pp. 2863-2876
Author(s):  
CARLOS LEIVA
Keyword(s):  
Dimensional Reduction ◽  
Relativistic Particle ◽  
Dimensional Space ◽  
Lorentz Invariance ◽  
Conformal Group ◽  
Reduction Procedure ◽  
Doubly Special Relativity ◽  
Nonlinear Algebra ◽  
Space Dynamics ◽  
The One

The relation between conformal generators and Magueijo–Smolin Doubly Special Relativity term, is achieved. Through a dimensional reduction procedure, it is demonstrated that a massless relativistic particle living in a d-dimensional space, is isomorphic to the one living in a d+2 space with pure Lorentz invariance and to a particle living in a AdS d+1 space. To accomplish these identifications, the conformal group is extended and a nonlinear algebra is obtained. Finally, because the relation between momenta and velocities is known through the dimensional reduction procedure, the problem of position space dynamics is solved.

scholarly journals CONFORMAL GENERATORS AND DOUBLY SPECIAL RELATIVITY THEORIES

2005 ◽  
Vol 20 (11) ◽  
pp. 861-867 ◽  
Author(s):  
CARLOS LEIVA
Keyword(s):  
Special Relativity ◽  
Linear Combination ◽  
Dimensional Reduction ◽  
Light Cone ◽  
Massless Particle ◽  
Conformal Group ◽  
Cone Structure ◽  
Doubly Special Relativity

In this paper, the relation between the modified Lorenz boosts, proposed in the doubly relativity theories and a linear combination of Conformal Group generators in R1,d-1 is investigated. The introduction of a new generator is proposed in order to deform the Conformal Group to achieve the connection conjectured. The new generator is obtained through a formal dimensional reduction from a free massless particle living in a R2,d space. Due to this treatment it is possible to say that even DSR theories modify light-cone structure in R1,d-1, it could remains, in some cases, untouched in R2,d.

scholarly journals ELEMENTARY PARTICLE INTERACTION FROM A KALUZA-KLEIN SCHEME

2008 ◽  
Vol 23 (08) ◽  
pp. 1182-1189
Author(s):  
FRANCESCO CIANFRANI ◽  
GIOVANNI MONTANI
Keyword(s):  
Elementary Particle ◽  
Dimensional Reduction ◽  
Dimensional Space ◽  
Particle Interaction ◽  
Gauge Coupling ◽  
Space Time ◽  
Reduction Procedure ◽  
Weak Model ◽  
Dimensional Space Time ◽  
Kaluza Klein

We discuss properties of particles and fields in a multi-dimensional space-time, where the geometrization of gauge interactions can be performed. As far as spinors are concerned, we outline how the gauge coupling can be recognized by a proper dependence on extra-coordinates and by the dimensional reduction procedure. Finally applications to the Electro-Weak model are presented.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

Success probabilities for second guessers

1980 ◽  
Vol 17 (04) ◽  
pp. 1133-1137 ◽  
Author(s):  
A. O. Pittenger
Keyword(s):  
Lower Bound ◽  
Dimensional Space ◽  
Success Probability ◽  
First Person ◽  
True Location ◽  
Rotationally Symmetric ◽  
The One ◽  
Sharp Lower Bound

Two people independently and with the same distribution guess the location of an unseen object in n-dimensional space, and the one whose guess is closer to the unseen object is declared the winner. The first person announces his guess, but the second modifies his unspoken idea by moving his guess in the direction of the first guess and as close to it as possible. It is shown that if the distribution of guesses is rotationally symmetric about the true location of the unseen object, ¾ is the sharp lower bound for the success probability of the second guesser. If the distribution is fixed and the dimension increases, then for a certain class of distributions, the success probability approaches 1.

scholarly journals New metric to quantify the similarity between planetary systems: application to dimensionality reduction using T-SNE

2019 ◽  
Vol 624 ◽  
pp. A45 ◽  
Author(s):  
Y. Alibert
Keyword(s):  
Dimensionality Reduction ◽  
Dimensional Space ◽  
Random Systems ◽  
Planetary Systems ◽  
Machine Learning Techniques ◽  
Underlying Structure ◽  
Population Synthesis ◽  
Learning Techniques ◽  
The One ◽  
Protoplanetary Discs

Context. Planet formation models now often consider the formation of planetary systems with more than one planet per system. This raises the question of how to represent planetary systems in a convenient way (e.g. for visualisation purpose) and how to define the similarity between two planetary systems, for example to compare models and observations. Aims. We define a new metric to infer the similarity between two planetary systems, based on the properties of planets that belong to these systems. We then compare the similarity of planetary systems with the similarity of protoplanetary discs in which they form. Methods. We first define a new metric based on mixture of Gaussians, and then use this metric to apply a dimensionality reduction technique in order to represent planetary systems (which should be represented in a high-dimensional space) in a two-dimensional space. This allows us study the structure of a population of planetary systems and its relation with the characteristics of protoplanetary discs in which planetary systems form. Results. We show that the new metric can help to find the underlying structure of populations of planetary systems. In addition, the similarity between planetary systems, as defined in this paper, is correlated with the similarity between the protoplanetary discs in which these systems form. We finally compare the distribution of inter-system distances for a set of observed exoplanets with the distributions obtained from two models: a population synthesis model and a model where planetary systems are constructed by randomly picking synthetic planets. The observed distribution is shown to be closer to the one derived from the population synthesis model than from the random systems. Conclusions. The new metric can be used in a variety of unsupervised machine learning techniques, such as dimensionality reduction and clustering, to understand the results of simulations and compare them with the properties of observed planetary systems.

scholarly journals Storage Efficient Trajectory Clustering and k-NN for Robust Privacy Preserving Spatio-Temporal Databases

Algorithms ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 266 ◽  
Author(s):  
Elias Dritsas ◽  
Andreas Kanavos ◽  
Maria Trigka ◽  
Spyros Sioutas ◽  
Athanasios Tsakalidis
Keyword(s):  
Privacy Preservation ◽  
Dimensional Space ◽  
Research Work ◽  
Temporal Databases ◽  
Mobile Object ◽  
Linear Component ◽  
Trajectory Data ◽  
Spatio Temporal ◽  
Storage Problem ◽  
The One

The need to store massive volumes of spatio-temporal data has become a difficult task as GPS capabilities and wireless communication technologies have become prevalent to modern mobile devices. As a result, massive trajectory data are produced, incurring expensive costs for storage, transmission, as well as query processing. A number of algorithms for compressing trajectory data have been proposed in order to overcome these difficulties. These algorithms try to reduce the size of trajectory data, while preserving the quality of the information. In the context of this research work, we focus on both the privacy preservation and storage problem of spatio-temporal databases. To alleviate this issue, we propose an efficient framework for trajectories representation, entitled DUST (DUal-based Spatio-temporal Trajectory), by which a raw trajectory is split into a number of linear sub-trajectories which are subjected to dual transformation that formulates the representatives of each linear component of initial trajectory; thus, the compressed trajectory achieves compression ratio equal to M : 1 . To our knowledge, we are the first to study and address k-NN queries on nonlinear moving object trajectories that are represented in dual dimensional space. Additionally, the proposed approach is expected to reinforce the privacy protection of such data. Specifically, even in case that an intruder has access to the dual points of trajectory data and try to reproduce the native points that fit a specific component of the initial trajectory, the identity of the mobile object will remain secure with high probability. In this way, the privacy of the k-anonymity method is reinforced. Through experiments on real spatial datasets, we evaluate the robustness of the new approach and compare it with the one studied in our previous work.

DIMENSIONAL REDUCTION AND THE LANCZOS TENSOR

1989 ◽  
Vol 04 (28) ◽  
pp. 2739-2746 ◽  
Author(s):  
M.D. ROBERTS
Keyword(s):  
Dimensional Reduction ◽  
Weyl Tensor ◽  
Weak Field ◽  
Vacuum Field ◽  
Linear Wave ◽  
Field Equations ◽  
Weak Field Limit ◽  
Magnetic Theory ◽  
Electro Magnetic ◽  
The One

The Lanczos tensor Hαβγ is a potential for the Weyl tensor. Given the symmetries of these tensors it would be expected that the identification Hαβ5=Fαβ would give a reduction of the five dimensional vacuum field equations into equations related to the Einstein Maxwell equation, it is shown that this does not happen; furthermore it is shown that there is no dimensional reduction scheme involving the Lanczos tensor which agrees with the one devised by Kaluza and Klein in the weak field limit. The covariant derivative of the Weyl tensor can be expressed as a type of non-linear wave equation in the Lanczos tensor, the literature contains two incorrect expressions for this equation, here the correct expression is given for the first time. The expression for the Lanczos tensor in the case of weak fields is generalized. Some remarks are made on other approaches to include electro-magnetic theory into the theory of the Lanczos tensor.

scholarly journals One-loop nonbirefringent effects on the electromagnetic vertex in the Standard Model Extension

2014 ◽  
Vol 29 (22) ◽  
pp. 1450107 ◽  
Author(s):  
A. Moyotl ◽  
H. Novales-Sanchez ◽  
J. J. Toscano ◽  
E. S. Tututi
Keyword(s):  
Standard Model ◽  
Lorentz Invariance ◽  
Lorentz Violation ◽  
Tree Level ◽  
Isotropic Case ◽  
Photon Propagator ◽  
Standard Model Extension ◽  
Model Extension ◽  
The One ◽  
Electromagnetic Vertex

Lorentz violation emerged from a fundamental description of nature may impact, at low energies, the Maxwell sector, so that contributions from such new physics to the electromagnetic vertex would be induced. Particularly, nonbirefringent CPT-even effects from the electromagnetic sector modified by the Lorentz- and CPT-violating Standard Model Extension alter the structure of the free photon propagator. We calculate Lorentz-violating contributions to the electromagnetic vertex, at the one-loop level, by using a modified photon propagator carrying this sort of effects. We take the photon off shell, and find an expression that involves both isotropic and anisotropic effects of nonbirefringent violation of Lorentz invariance. Our analysis of the one-loop vertex function includes gauge invariance, transformation properties under C, P and T, and tree-level contributions from Lorentz-violating nonrenormalizable interactions. These elements add to previous studies of the one-loop contributions to the electromagnetic vertex in the context of Lorentz violation in the photon sector. Finally, we restrict our analysis to the isotropic case and derive a finite contribution from isotropic Lorentz violation to the anomalous magnetic moment of fermions that coincides with the result already reported in the literature.

scholarly journals Paramagnetic versus Diamagnetic Interaction in the SU(2) Higgs Model

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1237
Author(s):  
Dmitry Antonov
Keyword(s):  
Gauge Boson ◽  
Effective Action ◽  
Dimensional Reduction ◽  
Higgs Model ◽  
Analytic Calculation ◽  
Standard Result ◽  
Correlation Lengths ◽  
Yang Mills ◽  
Diamagnetic Contribution ◽  
The One

We present an analytic calculation of the paramagnetic and diamagnetic contributions to the one-loop effective action in the SU(2) Higgs model. The paramagnetic contribution is produced by the gauge boson, while the diamagnetic contribution is produced by the gauge boson and the ghost. In the limit, where these particles are massless, the standard result of - 12 for the ratio of the paramagnetic to the diamagnetic contribution is reproduced. If the mass of the gauge boson and the ghost become much larger than the inverse vacuum correlation lengths of the Yang–Mills vacuum, the value of the ratio goes to - 8 . We also find that the same values of the ratio are achieved in the deconfinement phase of the model, up to the temperatures at which the dimensional reduction occurs.

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