The Rotation Group

1980 ◽  
pp. 185-231
Author(s):  
T. Hida
Keyword(s):  
Rotation Group

Some properties of Wigner coefficients and hyperspherical harmonics

1956 ◽  
Vol 52 (3) ◽  
pp. 424-430 ◽  
Author(s):  
A. P. Stone
Keyword(s):  
Angular Momentum ◽  
Euclidean Space ◽  
Rotation Group ◽  
Dimensional Euclidean Space ◽  
Hyperspherical Harmonics ◽  
Shift Operators ◽  
Analytical Relations

ABSTRACTGeneral shift operators for angular momentum are obtained and applied to find closed expressions for some Wigner coefficients occurring in a transformation between two equivalent representations of the four-dimensional rotation group. The transformation gives rise to analytical relations between hyperspherical harmonics in a four-dimensional Euclidean space.

Experimental classification of multi-spin coherence under the full rotation group

1988 ◽  
Vol 144 (4) ◽  
pp. 328-332 ◽  
Author(s):  
D. Suter ◽  
J.G. Pearson
Keyword(s):  
Rotation Group ◽  
Spin Coherence ◽  
Full Rotation

2D ELASTICITY TENSOR INVARIANTS, INVARIANTS DEFINITE POSITIVE CRITERIA

2021 ◽  
Vol 10 (8) ◽  
pp. 2999-3012
Author(s):  
K. Atchonouglo ◽  
G. de Saxcé ◽  
M. Ban
Keyword(s):  
Group Action ◽  
Linear Elasticity ◽  
Orbit Space ◽  
Rotation Group ◽  
Elasticity Tensor ◽  
Tensor Invariants ◽  
Material Classification ◽  
The One ◽  
2D Elasticity ◽  
Space Description

In this paper, we constructed relationships with the differents 2D elasticity tensor invariants. Indeed, let ${\bf A}$ be a 2D elasticity tensor. Rotation group action leads to a pair of Lax in linear elasticity. This pair of Lax leads to five independent invariants chosen among six. The definite positive criteria are established with the determined invariants. We believe that this approach finds interesting applications, as in the one of elastic material classification or approaches in orbit space description.

scholarly journals Orthogonal Isomorphic Representations Of Free Groups

1956 ◽  
Vol 8 ◽  
pp. 256-262 ◽  
Author(s):  
J. De Groot
Keyword(s):  
Euclidean Space ◽  
Free Groups ◽  
Three Dimensional ◽  
Rotation Group ◽  
Dimensional Euclidean Space ◽  
Orthogonal Matrices ◽  
Abelian Subgroups ◽  
Proper Orthogonal

1. Introduction. We consider the group of proper orthogonal transformations (rotations) in three-dimensional Euclidean space, represented by real orthogonal matrices (aik) (i, k = 1,2,3) with determinant + 1 . It is known that this rotation group contains free (non-abelian) subgroups; in fact Hausdorff (5) showed how to find two rotations P and Q generating a group with only two non-trivial relationsP2 = Q3 = I.

scholarly journals Infinite dimensional rotations and Laplacians in terms of white noise calculus

1992 ◽  
Vol 128 ◽  
pp. 65-93 ◽  
Author(s):  
Takeyuki Hida ◽  
Nobuaki Obata ◽  
Kimiaki Saitô
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Quantum Physics ◽  
Variational Calculus ◽  
Rotation Group ◽  
Infinite Dimensional ◽  
Lévy Laplacian ◽  
White Noise Functionals ◽  
White Noise Calculus

The theory of generalized white noise functionals (white noise calculus) initiated in [2] has been considerably developed in recent years, in particular, toward applications to quantum physics, see e.g. [5], [7] and references cited therein. On the other hand, since H. Yoshizawa [4], [23] discussed an infinite dimensional rotation group to broaden the scope of an investigation of Brownian motion, there have been some attempts to introduce an idea of group theory into the white noise calculus. For example, conformal invariance of Brownian motion with multidimensional parameter space [6], variational calculus of white noise functionals [14], characterization of the Levy Laplacian [17] and so on.

scholarly journals Nonignorable Nonresponse Imputation and Rotation Group Bias Estimation on the Rotation Sample Survey

2008 ◽  
Vol 21 (3) ◽  
pp. 361-375 ◽  
Author(s):  
Bo-Seung Choi ◽  
Dae-Young Kim ◽  
Kee-Whan Kim ◽  
You-Sung Park
Keyword(s):  
Rotation Group ◽  
Sample Survey ◽  
Bias Estimation ◽  
Nonignorable Nonresponse

scholarly journals Mass generation in QCD — Oscillating quarks and gluons

2014 ◽  
Vol 29 (21) ◽  
pp. 1444015
Author(s):  
Peter Minkowski
Keyword(s):  
Harmonic Oscillator ◽  
Gauge Boson ◽  
Rotation Group ◽  
Broken Symmetry ◽  
Mass Generation ◽  
Symmetry Classification ◽  
Angular Momenta ◽  
Comparable Level ◽  
Space Rotation

The present lecture is devoted to embedding the approximate genuine harmonic oscillator structure of valence [Formula: see text] mesons and in more detail the qqq configurations for u, d, s flavored baryons in QCD for three light flavors of quark. It includes notes, preparing the counting of "oscillatory modes of N fl = 3 light quarks, u, d, s in baryons," using the [Formula: see text] broken symmetry classification, extended to the harmonic oscillator symmetry of 3 paired oscillator modes. [Formula: see text] stands for the space rotation group generated by the sum of the 3 individual angular momenta of quarks in their c.m. system. The oscillator extension to valence gauge boson states is not yet developed to a comparable level.

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