Complex Angular Momenta and Many‐Particle States. I. Properties of Local Representations of the Rotation Group

1964 ◽  
Vol 5 (10) ◽  
pp. 1391-1400 ◽  
Author(s):  
M. Andrews ◽  
J. Gunson
Keyword(s):  
Rotation Group ◽  
Angular Momenta ◽  
Local Representations

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.

Counting of oscillatory modes of valence quarks forming qqq baryons for three quark flavors u, d, s

2017 ◽  
Vol 32 (04) ◽  
pp. 1750004 ◽  
Author(s):  
Sonia Kabana ◽  
Peter Minkowski
Keyword(s):  
Field Theory ◽  
Finite Number ◽  
Center Of Mass ◽  
Rotation Group ◽  
Broken Symmetry ◽  
Mass System ◽  
Angular Momenta ◽  
Space Rotation ◽  
Three Space ◽  
Quark Flavors

We present the unique properties of oscillatory modes of [Formula: see text] light quarks — [Formula: see text], [Formula: see text], [Formula: see text] — using the [Formula: see text] broken symmetry classification. [Formula: see text] stands for the space rotation group generated by the sum of the three individual angular momenta of quarks in their c.m. system. The baryonic multiplets are shown to emerge from the picture of oscillating quarks in three space dimensions in the center-of-mass system of the baryons. All oscillatory modes are fully relativistic with a finite number of oscillators and this is forming the unique harmonic oscillator with these properties. The density of states as a function of mass-square is calculated. This estimate is of relevance for the accounting of the missing states of unobserved hadrons, as the here estimated baryonic multiplets include both the observed and the unobserved (or “missing”) hadrons. The estimate is conceptually different from Hagedorn’s model and is based on field theory of QCD.

The vector-ladder operators for the rotation group O3

1993 ◽  
Vol 71 (3-4) ◽  
pp. 152-154
Author(s):  
J. E. Hardy
Keyword(s):  
Rotation Group ◽  
Matrix Elements ◽  
Ladder Operators ◽  
Straightforward Calculation ◽  
Angular Momenta ◽  
State Formula

The two vector-ladder operators, which step from any state [Formula: see text] in an irreducible multiplet in the space of product states of two commuting angular momenta, are defined and all their nonvanishing matrix elements are given, facilitating direct, straightforward calculation of the six nearby nonsibling states [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text].

Photonic quantum Hall effect and multiplexed light sources of large orbital angular momenta

2021 ◽  
Author(s):  
Babak Bahari ◽  
Liyi Hsu ◽  
Si Hui Pan ◽  
Daryl Preece ◽  
Abdoulaye Ndao ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Light Sources ◽  
Angular Momenta

scholarly journals Spin-decoupled metasurface for simultaneous detection of spin and orbital angular momenta via momentum transformation

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Yinghui Guo ◽  
Shicong Zhang ◽  
Mingbo Pu ◽  
Qiong He ◽  
Jinjin Jin ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Simultaneous Detection ◽  
Single Element ◽  
Single Shot ◽  
Single Spin ◽  
Dual Functional ◽  
Angular Momenta ◽  
Quadratic Phase ◽  
Mode Space ◽  
Optical Configuration

AbstractWith inherent orthogonality, both the spin angular momentum (SAM) and orbital angular momentum (OAM) of photons have been utilized to expand the dimensions of quantum information, optical communications, and information processing, wherein simultaneous detection of SAMs and OAMs with a single element and a single-shot measurement is highly anticipated. Here, a single azimuthal-quadratic phase metasurface-based photonic momentum transformation (PMT) is illustrated and utilized for vortex recognition. Since different vortices are converted into focusing patterns with distinct azimuthal coordinates on a transverse plane through PMT, OAMs within a large mode space can be determined through a single-shot measurement. Moreover, spin-controlled dual-functional PMTs are proposed for simultaneous SAM and OAM sorting, which is implemented by a single spin-decoupled metasurface that merges both the geometric phase and dynamic phase. Interestingly, our proposed method can detect vectorial vortices with both phase and polarization singularities, as well as superimposed vortices with a certain interval step. Experimental results obtained at several wavelengths in the visible band exhibit good agreement with the numerical modeling. With the merits of ultracompact device size, simple optical configuration, and prominent vortex recognition ability, our approach may underpin the development of integrated and high-dimensional optical and quantum systems.

scholarly journals Circular polariton currents with integer and fractional orbital angular momenta

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
E. S. Sedov ◽  
V. A. Lukoshkin ◽  
V. K. Kalevich ◽  
P. G. Savvidis ◽  
A. V. Kavokin
Keyword(s):  
Angular Momenta

scholarly journals Integrated structured light architectures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Randy Lemons ◽  
Wei Liu ◽  
Josef C. Frisch ◽  
Alan Fry ◽  
Joseph Robinson ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Temporal Distribution ◽  
Multiple Degrees Of Freedom ◽  
Beam Combination ◽  
Angular Momenta ◽  
Field Control ◽  
Topological States ◽  
Spatio Temporal ◽  
Temporal Field ◽  
Structural Versatility

AbstractThe structural versatility of light underpins an outstanding collection of optical phenomena where both geometrical and topological states of light can dictate how matter will respond or display. Light possesses multiple degrees of freedom such as amplitude, and linear, spin angular, and orbital angular momenta, but the ability to adaptively engineer the spatio-temporal distribution of all these characteristics is primarily curtailed by technologies used to impose any desired structure to light. We demonstrate a laser architecture based on coherent beam combination offering integrated spatio-temporal field control and programmability, thereby presenting unique opportunities for generating light by design to exploit its topology.

scholarly journals Multi-granularity Deep Local Representations for Irregular Scene Text Recognition

2021 ◽  
Vol 2 (2) ◽  
pp. 1-18
Author(s):  
Hongchao Gao ◽  
Yujia Li ◽  
Jiao Dai ◽  
Xi Wang ◽  
Jizhong Han ◽  
...  
Keyword(s):  
State Of The Art ◽  
Visual Representation ◽  
Text Recognition ◽  
Natural Scene ◽  
Attention Network ◽  
Training Time ◽  
Scene Text ◽  
Benchmark Datasets ◽  
Local Representations ◽  
Scene Text Recognition

Recognizing irregular text from natural scene images is challenging due to the unconstrained appearance of text, such as curvature, orientation, and distortion. Recent recognition networks regard this task as a text sequence labeling problem and most networks capture the sequence only from a single-granularity visual representation, which to some extent limits the performance of recognition. In this article, we propose a hierarchical attention network to capture multi-granularity deep local representations for recognizing irregular scene text. It consists of several hierarchical attention blocks, and each block contains a Local Visual Representation Module (LVRM) and a Decoder Module (DM). Based on the hierarchical attention network, we propose a scene text recognition network. The extensive experiments show that our proposed network achieves the state-of-the-art performance on several benchmark datasets including IIIT-5K, SVT, CUTE, SVT-Perspective, and ICDAR datasets under shorter training time.

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