scholarly journals Spin angular momentum of proton spin puzzle in complex octonion spaces

2017 ◽  
Vol 14 (07) ◽  
pp. 1750102 ◽  
Author(s):  
Zi-Hua Weng
Keyword(s):  
Electromagnetic Field ◽  
Quantum Mechanics ◽  
Dipole Moment ◽  
Angular Momentum ◽  
Angular Velocity ◽  
Orbital Angular Momentum ◽  
Magnetic Dipole Moment ◽  
Proton Spin ◽  
Spin Angular Momentum ◽  
Precessional Motion

The paper focuses on considering some special precessional motions as the spin motions, separating the octonion angular momentum of a proton into six components, elucidating the proton angular momentum in the proton spin puzzle, especially the proton spin, decomposition, quarks and gluons, and polarization and so forth. Maxwell was the first to use the quaternions to study the electromagnetic fields. Subsequently the complex octonions are utilized to depict the electromagnetic field, gravitational field, and quantum mechanics and so forth. In the complex octonion space, the precessional equilibrium equation infers the angular velocity of precession. The external electromagnetic strength may induce a new precessional motion, generating a new term of angular momentum, even if the orbital angular momentum is zero. This new term of angular momentum can be regarded as the spin angular momentum, and its angular velocity of precession is different from the angular velocity of revolution. The study reveals that the angular momentum of the proton must be separated into more components than ever before. In the proton spin puzzle, the orbital angular momentum and magnetic dipole moment are independent of each other, and they should be measured and calculated respectively.

On the theory of spinning particles

1947 ◽  
Vol 43 (1) ◽  
pp. 106-117 ◽  
Author(s):  
S. Shanmugadhasan
Keyword(s):  
Electromagnetic Field ◽  
Dipole Moment ◽  
Angular Momentum ◽  
Quantum Theory ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Hamiltonian Equation ◽  
Hamiltonian Form ◽  
Spin Angular Momentum ◽  
Spinning Particle

A classical theory of a spinning particle with charge and dipole moment in an electromagnetic field is obtained by working symmetrically with respect to retarded and advanced fields, and with respect to the ingoing and outgoing fields. The equations are in a simpler form than those of Bhabha and Corben or those of Bhabha, and involve fewer constants. On the assumption that the spin angular momentum tensor θμν satisfies the equation θ2 ≡ θμν θμν = constant, the value of the dipole moment Zμν is chosen to be Cθμν, where C is a constant. The theory is generalized to the case of several particles with charge and dipole moment. By using a suitable Hamiltonian equation, the classical equations of motion, obtained on the assumption that θ is a constant, are put into Hamiltonian form by means of the ‘Wentzel field’ and the λ-limiting process. The passage to the quantum theory is effected by the usual rules of quantization. The theory is extended to the case of particles with charge and dipole moment in the generalized wave field by defining the Wentzel potential in terms of the generalized relativistic δ-function.

scholarly journals The Spin Structure of the Nucleon

2016 ◽  
Vol 40 ◽  
pp. 1660001
Author(s):  
Xiangdong Ji ◽  
Yong Zhao
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Deeply Virtual Compton Scattering ◽  
Virtual Compton Scattering ◽  
Proton Spin ◽  
Effective Theory ◽  
Large Momentum ◽  
Theory Approach ◽  
The One ◽  
The Relationship

We justify the physical meaning of the spin and orbital angular momentum of free partons in the infinite momentum frame, and discuss the relationship between the Jaffe-Manohar and Ji’s sum rules for proton spin. The parton orbital angular momentum in the Jaffe-Manohar sum rule can be measured through twist-three GPD’s in hard scattering processes such as deeply virtual Compton scattering. Furthermore, we propose that the paton orbital angular momentum as well as the gluon helicity can be calculated in lattice QCD through a large momentum effective theory approach, and provide all the one-loop matching conditions for the proton spin content in perturbative QCD.

scholarly journals Proper relativistic position operators in 1+1 and 2+1 dimensions

2020 ◽  
Vol 35 (18) ◽  
pp. 2050084
Author(s):  
Taeseung Choi
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Wave Equations ◽  
Position Operator ◽  
Spin Angular Momentum ◽  
Particle Position ◽  
Constant Of Motion ◽  
Mass Moment ◽  
Relativistic Position ◽  
Canonical Position

We have revisited the Dirac theory in [Formula: see text] and [Formula: see text] dimensions by using the covariant representation of the parity-extended Poincaré group in their native dimensions. The parity operator plays a crucial role in deriving wave equations in both theories. We studied two position operators, a canonical one and a covariant one that becomes the particle position operator projected onto the particle subspace. In [Formula: see text] dimensions the particle position operator, not the canonical position operator, provides the conserved Lorentz generator. The mass moment defined by the canonical position operator needs an additional unphysical spin-like operator to become the conserved Lorentz generator in [Formula: see text] dimensions. In [Formula: see text] dimensions, the sum of the orbital angular momentum given by the canonical position operator and the spin angular momentum becomes a constant of motion. However, orbital and spin angular momentum do not conserve separately. On the other hand the orbital angular momentum given by the particle position operator and its corresponding spin angular momentum become a constant of motion separately.

scholarly journals Special Issue on Novel Insights into Orbital Angular Momentum Beams: From Fundamentals, Devices to Applications

2019 ◽  
Vol 9 (13) ◽  
pp. 2600 ◽  
Author(s):  
Yang Yue ◽  
Hao Huang ◽  
Yongxiong Ren ◽  
Zhongqi Pan ◽  
Alan E. Willner
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Elementary Particles ◽  
Spin Angular Momentum ◽  
Special Issue

It is well-known now that angular momentum carried by elementary particles can be categorized as spin angular momentum (SAM) and orbital angular momentum (OAM) [...]

scholarly journals SPIN AND ORBITAL ANGULAR MOMENTUM IN THE PROTON

2009 ◽  
Vol 18 (05n06) ◽  
pp. 1116-1134 ◽  
Author(s):  
ANTHONY W. THOMAS
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Current Data ◽  
Proton Spin ◽  
Current Status ◽  
Nucleon Structure ◽  
Upper Limits ◽  
European Muon Collaboration ◽  
Spin Crisis

Since the announcement of the proton spin crisis by the European Muon Collaboration there has been considerable progress in unravelling the distribution of spin and orbital angular momentum within the proton. We review the current status of the problem, showing that not only have strong upper limits have been placed on the amount of polarized glue in the proton but that the experimental determination of the spin content has become much more precise. It is now clear that the origin of the discrepancy between experiment and the naive expectation of the fraction of spin carried by the quarks and anti-quarks in the proton lies in the non-perturbative structure of the proton. We explain how the features expected in a modern, relativistic and chirally symmetric description of nucleon structure naturally explain the current data. The consequences of this explanation for the presence of orbital angular momentum on quarks and gluons is reviewed and comparison made with recent results from lattice QCD and experimental data.

The Quantum Mechanics of Cohesion

2007 ◽  
Vol 72 (2) ◽  
pp. 252-268
Author(s):  
Roy McWeeny
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Angular Momentum ◽  
Scalar Product ◽  
Hydrogen Molecule ◽  
Fundamental Problem ◽  
Ionic Species ◽  
General Context ◽  
Spin Angular Momentum ◽  
Actual Nature

We consider the fundamental problem of "what makes atoms stick together in molecules, crystals, or clusters?" The Heitler and London paper (1927) on the hydrogen molecule marked a first attempt to discuss, in terms of quantum mechanics, the interaction of two atoms with unpaired spins. The aim of this note is to show how the primitive concepts used eighty years ago still retain a certain validity even in a much more general context. We consider in fact the interaction of two arbitrary systems, each with a resultant spin angular momentum, and show how the interaction energy depends on the scalar product of the two resultants. The actual nature of the two systems is irrelevant: they may be atoms, molecules, or ionic species of any kind each described by a wave function which may be, in principle, exact. This provides a first step in the formulation of any general theory of cohesion.

scholarly journals Chern–Simons quantum mechanics and fractional angular momentum in atom system

2020 ◽  
Vol 35 (22) ◽  
pp. 2050122
Author(s):  
Yao-Yao Ma ◽  
Qiu-Yue Zhang ◽  
Qing Wang ◽  
Jian Jing
Keyword(s):  
Quantum Mechanics ◽  
Dipole Moment ◽  
Angular Momentum ◽  
Kinetic Energy ◽  
Energy Spectra ◽  
Reduced Model ◽  
Full Model ◽  
Specific Setting ◽  
Chern Simons ◽  
Atom System

The model of a planar atom which possesses a nonvanishing electric dipole moment interacting with magnetic fields in a specific setting is studied. Energy spectra of this model and its reduced model, which is the limit of cooling down the atom to the negligible kinetic energy, are solved exactly. We show that energy spectra of the reduced model cannot be obtained directly from the full ones by taking the same limit. In order to get the energy spectra of the reduced model from the full model, we must regularize energy spectra of the full model properly when the limit of the negligible kinetic energy is taken. It is one of the characteristics of the Chern–Simons quantum mechanics. Besides this, the canonical angular momentum of the reduced model will take fractional values although the full model can only take integers. It means that it is possible to realize the Chern–Simons quantum mechanics and fractional angular momentum simultaneously by this model.

An angular velocity sensor using machine learning and optical orbital angular momentum

2020 ◽  
Author(s):  
Elizabeth F. Strong ◽  
Alexander Q. Anderson ◽  
Brendan M. Heffernan ◽  
Michael P. Brenner ◽  
Juliet T. Gopinath ◽  
...  
Keyword(s):  
Machine Learning ◽  
Angular Momentum ◽  
Angular Velocity ◽  
Orbital Angular Momentum ◽  
Velocity Sensor

Arbitrary spin-to–orbital angular momentum conversion of light

Science ◽  
2017 ◽  
Vol 358 (6365) ◽  
pp. 896-901 ◽  
Author(s):  
Robert C. Devlin ◽  
Antonio Ambrosio ◽  
Noah A. Rubin ◽  
J. P. Balthasar Mueller ◽  
Federico Capasso
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Optical Communication ◽  
Arbitrary Spin ◽  
Spin States ◽  
Spin Angular Momentum ◽  
Optical Elements ◽  
Left And Right ◽  
General Material ◽  
Elliptically Polarized

Optical elements that convert the spin angular momentum (SAM) of light into vortex beams have found applications in classical and quantum optics. These elements—SAM-to–orbital angular momentum (OAM) converters—are based on the geometric phase and only permit the conversion of left- and right-circular polarizations (spin states) into states with opposite OAM. We present a method for converting arbitrary SAM states into total angular momentum states characterized by a superposition of independent OAM. We designed a metasurface that converts left- and right-circular polarizations into states with independent values of OAM and designed another device that performs this operation for elliptically polarized states. These results illustrate a general material-mediated connection between SAM and OAM of light and may find applications in producing complex structured light and in optical communication.

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