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Concept in differential geometry
a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in
Spin_structure
Property of protons and neutrons
particle physics, nucleon spin structure describes the partonic structure of nucleon (proton and neutron) intrinsic angular momentum (spin). The key question
Nucleon_spin_structure
Non-tensorial representation of the spin group
that admits a spin structure, one forms a spinor bundle associated to the principal spin bundle and a chosen spin representation; spinor fields are sections
Spinor
Special tangential structure
In spin geometry, a spinh structure (or quaternionic spin structure) is a generalization of a spin structure. In mathematics, these are used to describe
Spinh_structure
Special tangential structure
In spin geometry, a spinc structure (or complex spin structure) is a generalization of a spin structure. In mathematics, these are used to describe spinor
Spinc_structure
Geometric structure
a spin structure on an n {\displaystyle n} -dimensional orientable Riemannian manifold ( M , g ) , {\displaystyle (M,g),\,} one defines the spinor bundle
Spinor_bundle
Disordered magnetic state
direction; this is analogous to a crystal's lattice-based structure. The individual atomic bonds in a spin glass are a mixture of roughly equal numbers of ferromagnetic
Spin_glass
Double cover Lie group of the special orthogonal group
(non-existent) spin structures as calculation tool on (pseudo-)Riemannian manifolds: the spin group is the structure group of a spinor bundle. The affine
Spin_group
Relativistic interaction in quantum physics
mechanics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion
Spin–orbit_interaction
Intrinsic quantum property of particles
Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms
Spin_(physics)
Diagram used to represent quantum field theory calculations
Commons has media related to Spin networks. Spin connection Spin structure Character variety Penrose graphical notation Spin foam String-net Trace diagram
Spin_network
On the intersection form of a smooth, closed 4-manifold with a spin structure
theorem states that if a smooth, orientable, closed 4-manifold M has a spin structure (equivalently, if the second Stiefel–Whitney class w 2 ( M ) {\displaystyle
Rokhlin's_theorem
Mathematical concept
else the Cayley plane F4/Spin(9); see (Brendle & Schoen 2008). The odd-dimensional projective spaces can be given a spin structure, the even-dimensional
Complex_projective_space
Algebra based on a vector space with a quadratic form
matrices Hypercomplex number Octonion Paravector Quaternion Spin group Spin structure Spinor Spinor bundle Also known as a geometric algebra (especially over
Clifford_algebra
Spin 1 quasiparticle; quantum of a spin wave
spin structure of an electron in a crystal lattice. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave
Magnon
Unsolved physics problem
the quarks and gluons carry the spin of protons? More unsolved problems in physics The proton spin crisis (or proton spin puzzle) is a theoretical crisis
Proton_spin_crisis
Concept in differential geometry
M is orientable and admits a spin structure. It follows that the existence of a G 2 {\displaystyle G_{2}} -structure is much weaker than the existence
G2-structure
Formula for spinors
curvature, and results on spinors and spin structures. Given a spin structure on a pseudo-Riemannian manifold M and a spinor bundle S, the Lichnerowicz
Lichnerowicz_formula
Type of structure in atomic physics
Hyperfine structure contrasts with fine structure, which results from the interaction between the magnetic moments associated with electron spin and the
Hyperfine_structure
American DJ
Structure The Spin Dr. is the stage name of DJ Jonathan DePrisco. He spent his early career as a resident DJ at large NYC nightclubs including Limelight
Structure_the_Spin_Dr.
geometry, a metaplectic structure is the symplectic analog of spin structure on orientable Riemannian manifolds. A metaplectic structure on a symplectic manifold
Metaplectic_structure
Relativistic wave equation describing massless fermions
natural inhabitants of the spin structure are the Weyl spinors, in that the spin structure completely describes how the spinors behave under (Lorentz) boosts/rotations
Weyl_equation
Particular projective representations of the orthogonal or special orthogonal groups
the spin representations over the complex numbers first, and derive real representations by introducing real structures. The properties of the spin representations
Spin_representation
Structure group sub-bundle on a tangent frame bundle
-structure for the double cover Spin ( n ) → SO ( n ) {\displaystyle {\mbox{Spin}}(n)\to {\mbox{SO}}(n)} is a spin structure. (Note that the group homomorphism
G-structure_on_a_manifold
Type of subatomic particle
that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin 3/2, etc.) and obey the Pauli exclusion principle. These particles
Fermion
Model of hadrons
understand hadron structure by representing the parton distributions as functions of more variables, such as the transverse momentum and spin of the parton
Parton_(particle_physics)
1984 single by Dead or Alive
"You Spin Me Round (Like a Record)" is a song by the English pop band Dead or Alive. It was released on 5 November 1984, as the lead single from their
You Spin Me Round (Like a Record)
You_Spin_Me_Round_(Like_a_Record)
Topological structure in loop quantum gravity
In physics, the topological structure of spinfoam or spin foam consists of two-dimensional faces representing a configuration required by functional integration
Spin_foam
Quantum number parameterizing spin and angular momentum
the spin quantum number is a quantum number (designated s) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of
Spin_quantum_number
Details in the emission spectrum of an atom
In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to electron spin and relativistic corrections to the
Fine_structure
Magnetic phenomenon
In physics, the spin–spin relaxation is the mechanism by which Mxy, the transverse component of the magnetization vector, exponentially decays towards
Spin–spin_relaxation
Particle accelerator at Brookhaven National Laboratory in Upton, New York, USA
the universe shortly after the Big Bang. By colliding spin-polarized protons, the spin structure of the proton is explored. RHIC was the second-highest-energy
Relativistic Heavy Ion Collider
Relativistic_Heavy_Ion_Collider
Gamma matrices for arbitrary Clifford algebras
matrices for Weyl spinors. Gamma matrices also appear in generic settings in Riemannian geometry, particularly when a spin structure can be defined. Consider
Higher-dimensional gamma matrices
Higher-dimensional_gamma_matrices
Magnetic material under special conditions
abridged to "spin", which must satisfy in their low-energy state a "two-in, two-out" rule on each tetrahedron making the crystalline structure (see figure
Spin_ice
Class of spinors constructed using Clifford algebras
developed by Claude Chevalley. They are a key ingredient in the study of spin structures and higher dimensional generalizations of twistor theory, introduced
Pure_spinor
Mathematical description of fermions
geometric structure, including the geometry of the Lorentz group. Thus, much of what is said below can be applied to the Majorana equation. Dirac spinors are
Dirac_spinor
American physicist (1934–2024)
rule, the prototypical QCD spin sum rule. It states that in the Bjorken scaling domain, the integral of the spin structure function of the proton minus
James_Bjorken
Symmetry of physical laws under a charge-conjugation transformation
transform according to the spin group. Building a principle fiber bundle with the spin group as the fiber results in a spin structure. All that is missing in
C-symmetry
Type of magnetic state
down polarization of the spin. The band structure of an altermagnet. The altermagnetic spin polarization in band structure (energy–wavevector diagram)
Altermagnetism
Complex structures in matter physics
in water ice is found in the spin ices. A common spin ice structure is shown in Figure 6 in the cubic pyrochlore structure with one magnetic atom or ion
Geometrical_frustration
Relation between static and dynamic quantities
rule is the prototypical QCD spin sum rule. It states that in the Bjorken scaling domain, the integral of the spin structure function of the proton minus
Sum rules (quantum field theory)
Sum_rules_(quantum_field_theory)
International figure skating competition
The Golden Spin of Zagreb (Croatian: Zlatna pirueta Zagreba) is an annual figure skating competition sanctioned by the International Skating Union (ISU)
Golden_Spin_of_Zagreb
Scientific theory
depending on their spin, placing them into separate 'spin tetrahedra' to minimise the Pauli repulsions between electrons of the same spin. Introduced by J
Linnett_double-quartet_theory
Version without requiring the smooth manifolds involved to carry a complex structure
structure. Results of this kind were obtained by Michael Atiyah and Friedrich Hirzebruch in 1959, reducing the requirements to something like a spin structure
Riemann–Roch theorem for smooth manifolds
Riemann–Roch_theorem_for_smooth_manifolds
characteristics correspond bijectively to spin structures. Atiyah, Michael Francis (1971), "Riemann surfaces and spin structures", Annales Scientifiques de l'École
Theta_characteristic
Phenomenon involving the change of conductivity in metallic layers
electrons with various spin directions relative to the magnetization of the layers. Therefore, the equivalent circuit of the GMR structure consists of two parallel
Giant_magnetoresistance
Organized way in which molecules are ordered and sorted
When a molecule has an unpaired electron spin in a functional group of its structure, ENDOR and electron-spin resonance spectroscopes may also be performed
Chemical_structure
Classical theory of gravitation
Riemann–Cartan geometry. In particular, to be able to describe spinors requires the inclusion of a spin structure, which suffices to produce such a geometry. The chief
Einstein–Cartan_theory
Nesosilicate mineral species of garnet
group [[Ia3d]], with unit-cell parameter of 12.051 Å at 100 K. The spin structure of andradite contains two mutually canted equivalent antiferromagnetic
Andradite
Particle physics experiment
processes. The main physics goals are the investigation of the nucleon spin structure and hadron spectroscopy. The collaboration consists of 220 physicists
COMPASS_experiment
Site-directed spin labeling (SDSL) is a technique for investigating the structure and local dynamics of proteins using electron spin resonance. The theory
Site-directed_spin_labeling
Connection on a spinor bundle
In differential geometry and mathematical physics, a spin connection is a connection on a spinor bundle. It is induced, in a canonical manner, from the
Spin_connection
Spin-polarized scanning tunneling microscopy (SP-STM) is a type of scanning tunneling microscope (STM) that can provide detailed information of magnetic
Spin-polarized scanning tunneling microscopy
Spin-polarized_scanning_tunneling_microscopy
4-manifold invariants
the structure group from the connected component GL(4)+ to SO(4) and is harmless from a homotopical point of view. A spinc structure or complex spin structure
Seiberg–Witten_invariants
American high-energy nuclear physicist
nucleon spin structure in the journal Reviews of Modern Physics that has been cited over 200 times. She currently studies nucleon structure and quantum
Christine_Aidala
Type of energy exchange
high-resolution crystal structure determination of small molecules and proteins. In solid-state nuclear magnetic resonance, spin diffusion plays a major
Spin_diffusion
1979 single by Wings
"Spin It On" is a song written by Paul McCartney that was first released on Wings' 1979 album Back to the Egg. It was also issued as the B-side of the
Spin_It_On
Ordered arrangement of magnetic spins in a material
The term magnetic structure of a material pertains to the ordered arrangement of magnetic spins, typically within an ordered crystallographic lattice
Magnetic_structure
Gauge boson self-energy due to interactions with virtual particles
in quantum chromodynamics, as for example in considering the hadron spin structure. They yield a phase factor to the vacuum to vacuum transition amplitude
Vacuum_polarization
Technique of shooting liquid metal on cooled rotating drum
Melt spinning is a metal forming technique that is typically used to form thin ribbons of metal or alloys with a particular atomic structure. Some important
Melt_spinning
Spectroscopic technique based on change of nuclear spin state
of energy for parallel spins has to do with the quark structure of these two nucleons.[citation needed] As a result, the spin ground state for the deuteron
Nuclear_magnetic_resonance
Application of Lagrangian mechanics to field theories
manifold; this enables the concept of a spin structure, which, roughly speaking, is a way of formulating spinors consistently in a curved spacetime. The
Lagrangian_(field_theory)
Weak, attractive magnetism possessed by most elements and some compounds
However, in some cases a band structure can result in which there are two delocalized sub-bands with states of opposite spins that have different energies
Paramagnetism
Spin representations of the SO(3) group
In mathematics, the spinor concept as specialised to three dimensions can be treated by means of the traditional notions of dot product and cross product
Spinors_in_three_dimensions
Fiber bundle whose fibers are group torsors
\mathrm {SO} (n)\subseteq \mathrm {GL} (n,\mathbb {R} )} . A manifold has spin structure if and only if its frame bundle can be further reduced from S O ( n
Principal_bundle
Phase of matter
physics, a quantum spin liquid is a phase of matter that can be formed by interacting quantum spins in certain magnetic materials. Quantum spin liquids (QSL)
Quantum_spin_liquid
Equations describing classical electromagnetism
Ablamowicz, Rafał; Lounesto, Pertti (eds.), Clifford Algebras and Spinor Structures, Springer, pp. 265–280, doi:10.1007/978-94-015-8422-7_16, ISBN 978-90-481-4525-6
Maxwell's_equations
Spectrum of eigenvalues
Riemannian manifold with a spin structure. The isospectral problem for the Dirac spectrum asks whether two Riemannian spin manifolds have identical spectra
Dirac_spectrum
Ordered arrangement of atoms, ions, or molecules in a crystalline material
crystal structure, alteration in the electrical and thermal properties of the material may ensue. Impurities may also manifest as electron spin impurities
Crystal_structure
Type of biological prediction
tertiary structure from primary structure. Structure prediction is different from the inverse problem of protein design. Protein structure prediction
Protein_structure_prediction
on a compact spin manifold, acting on the Hilbert space of L2-spinors, accompanied by the Dirac operator associated to the spin structure. From the knowledge
Spectral_triple
Quantum process reducing the variance of spin along a particular axis
particles with spin. This is achieved by somehow entangling the individual spin states within the ensemble.The quantum states obtained are called spin squeezed
Spin_squeezing
Thin semiconductors
TMDs monolayer, MX2. In addition, the asymmetric structure of Janus MoSSe provides an enhanced Rashba spin–orbit interaction, which suggests asymmetrically
Transition metal dichalcogenide monolayers
Transition_metal_dichalcogenide_monolayers
Four-dimensional complete Riemannian manifold satisfying the vacuum Einstein equations
Rarita–Schwinger index (spin-3/2 index), or generally the Chern class. The ability to support a spin structure (i.e. to allow consistent Dirac spinors) is another
Gravitational_instanton
Phase of matter in superconductors
applied magnetic field, then the spin structure is not affected until the Zeeman energy is strong enough to flip one spin of the singlet and break the Cooper
Fulde–Ferrell–Larkin–Ovchinnikov phase
Fulde–Ferrell–Larkin–Ovchinnikov_phase
Concept in condensed matter physics
rigid crystal structure. It is a quantum of a sound wave. A magnon is a collective excitation associated with the electrons' spin structure in a crystal
Quasiparticle
Pakistani nuclear physicist and author (born 1950)
the quark-gluon structure of nuclei, quantum chromodynamics, and particle phenomenology. In particular this included the spin structure of nuclei and quark-gluon
Pervez_Hoodbhoy
Set of topological invariants
manifold M is orientable if and only if w1(M×R) = 0. The bundle admits a spin structure if and only if both the first and second Stiefel–Whitney classes are
Stiefel–Whitney_class
Spin polarization of atomic nuclei beyond thermal equilibrium
Other applications include determining the function of the neutron spin-structures by scattering polarized electrons from a very polarized target (3He)
Hyperpolarization_(physics)
Condensed matter phenomenon; vortex-like magnetic quasiparticle
further suggest that there must exist an energy term that stabilizes the spin-structure into a localized magnetic soliton whose energy is invariant by translation
Magnetic_skyrmion
Industrial procedure
widely used for the fabrication of planar photonic structures made of polymers.[citation needed] Spin coating is also sometimes used in the preparation
Spin_coating
Compact astronomical body
set out to apply the idea to stars. He assumed spherical symmetry with no spin and found a solution to Einstein's equations. A few months after Schwarzschild
Black_hole
Mineral supergroup
vibrations are strongly affected by spin ordering. These effects demonstrate how the crystallographic structure, magnetic frustration, and non-collinear
Spinel_group
Unique features in the electronic bands of a given material
the fine structure of atoms, where energy levels suffer from a similar effect from the non-relativistic calculation due to effects like spin–orbit interaction
Fine_electronic_structure
diffeomorphism Orientability characteristic class Chern class Pontrjagin class spin structure differentiable map submersion immersion Embedding Whitney embedding
List of differential geometry topics
List_of_differential_geometry_topics
algebra Complex spin structure Conformal manifold Conformally flat manifold Dirac operator Poincaré metric Spin group Spin structure Spinor bundle Ahlfors
Clifford_analysis
Regular pattern of magnetic moment ordering
(exchange) interactions between the magnetic moments or spins may lead to antiferromagnetic structures. In the simplest case, one may consider an Ising model
Antiferromagnetism
Fermion discretization with four doublers
Dirac spinor component. Denoting one of those components by χ n {\displaystyle \chi _{n}} , which is Grassmann variable with no spin structure, the other
Staggered_fermion
Technique for isolating and observing short-lived free radical molecules
Research, 1971, 4.,31." A detailed and structured list of Spin Traps by IUPAC Proniewski (2018). "Immuno-Spin Trapping-Based Detection of Oxidative Modifications
Spin_trapping
Model of interacting spinless bosons on a lattice
internal spin structure of atoms, for example due to trapping an entire degenerate manifold of hyperfine spin states (for F=1 it leads to the spin-1 Bose–Hubbard
Bose–Hubbard_model
Textile-spinning method that uses compressed air to twist fibers
Air-jet spinning (also called air spinning, jet spinning, or fasciated yarn spinning) is a method of spinning staple-fiber yarns in which a high-velocity
Air-jet_spinning
Triplet state of the dioxygen molecule
has a non-zero spin magnetic moment, oxygen is paramagnetic; i.e., it can be attracted to the poles of a magnet. Thus, the Lewis structure O=O with all
Triplet_oxygen
Way in which an organization is structured
start-ups, university spin offs). As companies grow they tend to become more complex and hierarchical, which lead to an expanded structure, with more levels
Organizational_structure
Type of conserved current
ISBN 978-0-201-50397-5. A. Deur, S. J. Brodsky, G. F. de Teramond (2019) “The Spin Structure of the Nucleon” Rept. Prog. Phys. 82 076201 Zuber, Kai (2020). Neutrino
Axial_current
Distribution used in collider collisions
{\displaystyle F_{1}(x)} and the quark spin probability distribution g 1 q ( x ) {\displaystyle g_{1}^{q}(x)} for the polarized structure functions g 1 ( x ) {\displaystyle
Transverse momentum distributions
Transverse_momentum_distributions
Technique for spinning yarn
in 1967. One disadvantage of open-end spinning is that it is limited to coarser counts, another is the structure of the yarn itself with fibres less in
Open-end_spinning
Derivative used in gauge theories
the gauge theory; and, for the case of spinors, the associated bundle would be a spin bundle of the spin structure. Although conceptually the same, this
Gauge_covariant_derivative
First-order differential linear operator on spinor bundle, whose square is the Laplacian
Physical Character. 117 (778): 610−624. doi:10.1098/rspa.1928.0023. "Spinor structure", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Jurgen Jost,
Dirac_operator
Italian supermarket chain
EuroSpin Viaggi brand. The Eurospin group is structured as follows: EuroSpin's sales network in 2024: Wikimedia Commons has media related to EuroSpin. Discount
Eurospin
Theorem in quantum mechanics
The spin–statistics theorem proves that the observed relationship between the intrinsic spin of a particle (angular momentum not due to the orbital motion)
Spin–statistics_theorem
SPIN STRUCTURE
SPIN STRUCTURE
Female/Male/Unisex
Korean
Korean name SHIN means "faith, trust." Compare with another form of Shin.
Boy/Male
British, Danish, English, Norwegian
Skin; Parchment
Biblical
rare; precious
Surname or Lastname
English
English : from Middle English spink ‘chaffinch’ (probably of imitative origin), hence a nickname bestowed on account of some fancied resemblance to the bird.
Girl/Female
Australian, Indian, Punjabi, Sikh
Quite and Gentle
Girl/Female
Muslim
Glowing skin
Male
Japanese
(1-晋, 2-信, 3-紳, 4-心, 5-慎, 6-新, 7-進, 8-真) Japanese name SHIN means 1) "advancing," 2) "belief," 3) "gentleman," 4) "heart," 5) "humble," 6) "new," 7) "progressive," and 8) "true." Compare with another form of Shin.
Male
Babylonian
, I trust in Sin!
Boy/Male
Egyptian
Light skin.
Boy/Male
Indian
Life Span
Surname or Lastname
English and Irish
English and Irish : (of Norman origin): habitational name from Épaignes in Eure, recorded in the Latin form Hispania in the 12th century. It seems to have been so called because it was established by colonists from Spain during the Roman Empire.English and Irish : habitational name from Espinay in Ille-et-Vilaine, Brittany, so called from a collective of Old French espine ‘thorn bush’.English and Irish : ethnic name for a Spaniard or, in the case of the Irish name, for someone returning from Spain (from Gaelic Spainneach ‘Spanish’); many Irish took refuge in Spain during the 17th century wars.
Biblical
a bush, enmity
Girl/Female
Australian, Biblical, Kurdish
Bush
Male
French
Old French name, possibly derived from the word pepin/pipin, PÉPIN means "seed of a fruit."
Girl/Female
Native American
Spins.
Boy/Male
Australian, Spanish
Innocent
Girl/Female
Biblical
Rare, precious.
Girl/Female
Christian, Hindu, Indian
Dark Skin
Boy/Male
Indian, Sanskrit
Skin of a Goat; Tiger Skin
Girl/Female
Indian
Glowing skin
SPIN STRUCTURE
SPIN STRUCTURE
Boy/Male
Tamil
Vimoksha | விமோகà¯à®·à®¾
Girl/Female
Australian, Chinese
Precious
Boy/Male
Egyptian
Mythical earth god.
Boy/Male
Hindu
The one who brought Ganga to earth, With glorious chariot
Girl/Female
Hindu, Indian, Punjabi, Sikh
Ranjha's Lover
Boy/Male
Muslim/Islamic
This was the name of the makes of astrolabes
Male
Hungarian
Pet form of Hungarian Péter, PETI means "rock, stone."
Boy/Male
Sikh
Worthy, Affectionate, Generous
Boy/Male
Hindu, Indian, Sanskrit
Human
Boy/Male
American, Australian, French, German, Portuguese, Spanish, Swiss, Teutonic
Illustrious Pledge; Shining Pledge; Pledge; Bright Promise; Spanish Form of Gilbert Hostage
SPIN STRUCTURE
SPIN STRUCTURE
SPIN STRUCTURE
SPIN STRUCTURE
SPIN STRUCTURE
a.
Full of spines; thorny; as, a spiny tree.
v. t.
To draw out tediously; to form by a slow process, or by degrees; to extend to a great length; -- with out; as, to spin out large volumes on a subject.
imp. & p. p.
of Spit
v. t.
To measure by the span of the hand with the fingers extended, or with the fingers encompassing the object; as, to span a space or distance; to span a cylinder.
imp.
of Spin
v. t.
To strip off the skin or hide of; to flay; to peel; as, to skin an animal.
n.
To thrust a spit through; to fix upon a spit; hence, to thrust through or impale; as, to spit a loin of veal.
v. t.
To draw out, and twist into threads, either by the hand or machinery; as, to spin wool, cotton, or flax; to spin goat's hair; to produce by drawing out and twisting a fibrous material.
n.
The act of spinning; as, the spin of a top; a spin a bicycle.
v. i.
To attend to a spit; to use a spit.
v. t.
To cover with skin, or as with skin; hence, to cover superficially.
v. i.
To practice spinning; to work at drawing and twisting threads; to make yarn or thread from fiber; as, the woman knows how to spin; a machine or jenny spins with great exactness.
v. i.
To move swifty; as, to spin along the road in a carriage, on a bicycle, etc.
n.
A sin offering; a sacrifice for sin.
a.
Like a spine in shape; slender.
v. t.
To cause to turn round rapidly; to whirl; to twirl; as, to spin a top.
imp. & p. p.
of Spin
v. t.
To protract; to spend by delays; as, to spin out the day in idleness.