Polar coordinates for a Dirac spinor and Bosonization

1985 ◽  
Vol 9 (4) ◽  
pp. 313-321 ◽  
Author(s):  
S. G. Mikhov
Keyword(s):  
Polar Coordinates ◽  
Dirac Spinor

scholarly journals Factorization of Dirac equation in two space dimensions

2014 ◽  
Vol 11 (04) ◽  
pp. 1450036 ◽  
Author(s):  
Hocine Bahlouli ◽  
Ahmed Jellal ◽  
Youness Zahidi
Keyword(s):  
Dirac Equation ◽  
Separation Of Variables ◽  
Scalar Potential ◽  
Complete Separation ◽  
Polar Coordinates ◽  
Dirac Spinor ◽  
Solvable Potentials ◽  
Scalar Type ◽  
Two Space Dimensions ◽  
Pseudo Scalar

We present a systematic approach for the separation of variables for the two-dimensional (2D) Dirac equation in polar coordinates. The three vector potential, which couple to the Dirac spinor via minimal coupling, along with the scalar potential are chosen to have angular dependence which emanate the Dirac equation to complete separation of variables. Exact solutions are obtained for a class of solvable potentials along with their relativistic spinor wavefunctions. Particular attention is paid to the situation where the potentials are confined to a quantum dot region and are of scalar, vector and pseudo-scalar type. The study of a single charged impurity embedded in a 2D Dirac equation in the presence of a uniform magnetic field was treated as a particular case of our general study.

Non-Polar Variation of Latitude

1972 ◽  
Vol 1 ◽  
pp. 93-101 ◽  
Author(s):  
S. Yumi
Keyword(s):  
Polar Motion ◽  
Polar Coordinates ◽  
Normal Variation ◽  
Latitude Variation ◽  
Local Trend

ABSTRACTAnalysing the residual latitude of the station, local trend in latitude variation other than by the polar motion was found.Residual latitude was calculated for each of 26 stations which gave the continuous records of observation during 6 years comprising — 1962 — 1967 as a difference between observed variation of latitude and – normal variation calculated by the polar coordinates Iderived from all the results of 26 stations.As far as the results during these six years are concerned, local trend at any station it seemed to be expressed in terms of 3λ.Assumed effect of local trend on the coordinates values of the instantaneous pole is also discussed.

The solution problem of Dirihle for equation of Laplace in polar coordinates by method Monte Carlo

2018 ◽  
Vol 2 ◽  
pp. 114-122
Author(s):  
Yu.I. Nikolayenko ◽  
◽  
V.G. Ilvovsky ◽  
S.V. Moiseenko ◽  
◽  
...  
Keyword(s):  
Monte Carlo ◽  
Polar Coordinates ◽  
Solution Problem

scholarly journals Gauge invariance, polar coordinates and inflation

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ali Akil ◽  
Xi Tong
Keyword(s):  
Coordinate System ◽  
Effective Potential ◽  
Gauge Invariance ◽  
Polar Coordinates ◽  
Quantum Corrections ◽  
Background Current ◽  
Gauge Invariant ◽  
Gauge Dependence ◽  
Current Term ◽  
Invariant Current

Abstract We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen’s gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.

scholarly journals Approach to hand posture recognition based on hand shape features for human–robot interaction

2021 ◽  
Author(s):  
Jing Qi ◽  
Kun Xu ◽  
Xilun Ding
Keyword(s):  
Gaussian Mixture ◽  
Human Robot Interaction ◽  
Polar Coordinates ◽  
Support Vector ◽  
Hand Posture ◽  
Data Set ◽  
Hand Shape ◽  
Hand Posture Recognition ◽  
Hand Segmentation ◽  
Posture Recognition

AbstractHand segmentation is the initial step for hand posture recognition. To reduce the effect of variable illumination in hand segmentation step, a new CbCr-I component Gaussian mixture model (GMM) is proposed to detect the skin region. The hand region is selected as a region of interest from the image using the skin detection technique based on the presented CbCr-I component GMM and a new adaptive threshold. A new hand shape distribution feature described in polar coordinates is proposed to extract hand contour features to solve the false recognition problem in some shape-based methods and effectively recognize the hand posture in cases when different hand postures have the same number of outstretched fingers. A multiclass support vector machine classifier is utilized to recognize the hand posture. Experiments were carried out on our data set to verify the feasibility of the proposed method. The results showed the effectiveness of the proposed approach compared with other methods.

scholarly journals Polar Coordinates View on KM-Arcs

2021 ◽  
Author(s):  
Kanat Abdukhalikov ◽  
Duy Ho
Keyword(s):  
Polar Coordinates

Finalization actions of the finalist teams in the Soccer World Cup 2018: a study with Polar Coordinates

2021 ◽  
Author(s):  
Juan Pablo Morillo-Baro ◽  
Rafael E. Reigal ◽  
José Antonio Ruíz-López ◽  
Juan Antonio Vázquez-Diz ◽  
Verónica Morales-Sánchez ◽  
...  
Keyword(s):  
Polar Coordinates ◽  
World Cup

63.35 An Exercise in Polar Coordinates

1981 ◽  
Vol 65 (434) ◽  
pp. 277
Author(s):  
K. C. May
Keyword(s):  
Polar Coordinates

The Expansion Model of Debris Cloud Induced by Oblique Hypervelocity Impact

2012 ◽  
Vol 13 (3-4) ◽  
Author(s):  
Qing-Ming Zhang ◽  
Y. H. Chen ◽  
F. L. Huang ◽  
Z. Z. Gong
Keyword(s):  
Conservation Law ◽  
Mass Conservation ◽  
Hypervelocity Impact ◽  
Polar Coordinates ◽  
Dynamic Evolution ◽  
Nonlinear Integral Equations ◽  
Simulation Code ◽  
Debris Cloud ◽  
Expansion Model ◽  
Energy Conservation Law

AbstractFor describing the dynamic evolution of debris cloud formed in oblique hypervelocity impact, a model (expressed in polar coordinates) for the shape, the velocity distribution and the mass distribution is developed according to the results of experiments and numerical simulation, and parameters of the Model are identified by nonlinear integral equations which are derived from mass conservation law and energy conservation law. Afterwards, the model has been verified by another simulation code.

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