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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
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
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
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
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
Double cover Lie group of the special orthogonal group
(non-existent) spin structures as a calculation tool on (pseudo-)Riemannian manifolds: the spin group is the structure group of a spinor bundle. The affine
Spin_group
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
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)
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
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
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
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.
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
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
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
geometry, a metaplectic structure is the symplectic analog of spin structure on orientable Riemannian manifolds. A metaplectic structure on a symplectic manifold
Metaplectic_structure
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
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 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
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
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
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
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
characteristics correspond bijectively to spin structures. Atiyah, Michael Francis (1971), "Riemann surfaces and spin structures", Annales Scientifiques de l'École
Theta_characteristic
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
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)
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
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
Chinese theoretical nuclear and particle physicist
in the quark and gluon structure of the proton and neutron in Quantum Chromodynamics (QCD). He formulated the spin structure of the proton in terms of
Xiangdong_Ji
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
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
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)
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
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)
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
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
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
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
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
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
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
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
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
American physicist, author and screenwriter (born 1954)
1016/0003-4916(80)90323-1. Mlodinow, L. D., and N. Papanicolaou (1981). "Pseudo-spin structure and large N expansion for a class of generalized helium Hamiltonians"
Leonard_Mlodinow
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
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
Topics referred to by the same term
free dictionary. A magnon is a collective excitation of the electrons' spin structure in a crystal lattice. Magnon may also refer to: Magnon, Gabon, a village
Magnon_(disambiguation)
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
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
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
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
2009 film by Gavin Hood
installment in the X-Men film series, the first Wolverine solo film, and a spin-off/prequel to X-Men (2000). The film was directed by Gavin Hood and written
X-Men_Origins:_Wolverine
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
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
American mathematical physicist (b. 1942)
782G. doi:10.1063/1.1705276. ISSN 0022-2488. Geroch, Robert (1968), "Spinor Structure of Space-Times in General Relativity. I", Journal of Mathematical Physics
Robert_Geroch
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
study the nucleon spin structure of simple nucleons like protons, neutrons or deuterons. In deep inelastic scattering the hadron structure is probed with
Polarized_target
Morgenstern, and R. Wiesendanger, “Direct observation of internal spin structure of magnetic vortex cores.,” Science, vol. 298, no. 5593, pp. 577–80
Magnetic_spin_vortex_disc
French mathematician (1919–1992)
mathematics at the Paul Sabatier University, known for his contributions to spinor structures and Clifford algebra. Crumeyrolle was a student of André Lichnerowicz
Albert_Crumeyrolle
Metastable phase of tungsten
in spintronic magnetic random access memories and spin-logic devices. β-W has a cubic A15 structure with space group P m 3 ¯ n {\displaystyle Pm{\bar
Beta-tungsten
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
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
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
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
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
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
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
Mineral supergroup
vibrations are strongly affected by spin ordering. These effects demonstrate how the crystallographic structure, magnetic frustration, and non-collinear
Spinel_group
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
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
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
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
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
2026 American action crime drama television series
A.T. Exiles is an American action drama series, that serves as a sequel/spin-off of the 2017 television series S.W.A.T.. Jason Ning serves as the series'
S.W.A.T._Exiles
Particle accelerator at DESY
HERA's longitudinally polarised electron beam was used to explore the spin structure of nucleons. For this purpose, the electrons were scattered at energies
HERA_(particle_accelerator)
Mathematical model of ferromagnetism in statistical mechanics
atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically
Ising_model
Type of Dirac operator eigenspinor
Killing spinor is a term used in mathematics and physics. By the more narrow definition, commonly used in mathematics, the term Killing spinor indicates
Killing_spinor
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
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
Class of materials
Spin gapless semiconductors are a class of materials in which the spin-averaged electronic band structure has no band gap, while the two spin channels
Spin_gapless_semiconductor
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
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
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
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
Mathematical model of magnetism
neighbour interactions determined by the alignment or anti-alignment of spin projections along the z {\displaystyle z} axis, as well as an external magnetic
Transverse-field_Ising_model
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
German automotive-technology company
exciting, connected and autonomous driving. It was formed in 2025 as a spin-off of Continental AG’s Automotive business. AUMOVIO develops hardware, software
Aumovio
Textile-spinning method that uses compressed air to twist fibers
The resulting yarn has a fasciated structure (a largely parallel core wrapped in twisted fibers). Air-jet spinning development initiated in the mid-1950s
Air-jet_spinning
algebra Complex spin structure Conformal manifold Conformally flat manifold Dirac operator Poincaré metric Spin group Spin structure Spinor bundle Ahlfors
Clifford_analysis
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
Branch of chemistry which studies 3D structure of molecules
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
Structural_chemistry
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)
Quantum mechanics principle
principle states that two or more identical particles with half-integer spins (i.e., fermions) cannot simultaneously occupy the same quantum state within
Pauli_exclusion_principle
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
Machinery used to spin cotton
Cotton-spinning machinery is machines which process (or spin) prepared cotton roving into workable yarn or thread. Such machinery can be dated back centuries
Cotton-spinning_machinery
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)
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
Airplane built by Anthony Fokker
The Fokker Spin was the first airplane built by Dutch aviation pioneer Anthony Fokker. The many bracing wires used to strengthen the aircraft made it resemble
Fokker_Spin
Neutron scattering technique
Neutron spin echo spectroscopy is an inelastic neutron scattering technique invented by Ferenc Mezei in the 1970s and developed in collaboration with John
Neutron_spin_echo
travel, tourism, insurance
SPIN STRUCTURE
SPIN STRUCTURE
Male
Babylonian
, I trust in Sin!
Male
French
Old French name, possibly derived from the word pepin/pipin, PÉPIN means "seed of a fruit."
Boy/Male
Indian, Sanskrit
Skin of a Goat; Tiger Skin
Girl/Female
Muslim
Glowing skin
Female/Male/Unisex
Korean
Korean name SHIN means "faith, trust." Compare with another form of Shin.
Girl/Female
Biblical
Rare, precious.
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.
Girl/Female
Australian, Indian, Punjabi, Sikh
Quite and Gentle
Girl/Female
Christian, Hindu, Indian
Dark Skin
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
Biblical
rare; precious
Girl/Female
Australian, Biblical, Kurdish
Bush
Girl/Female
Indian
Glowing skin
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.
Boy/Male
British, Danish, English, Norwegian
Skin; Parchment
Boy/Male
Australian, Spanish
Innocent
Girl/Female
Native American
Spins.
Boy/Male
Indian
Life Span
Boy/Male
Egyptian
Light skin.
SPIN STRUCTURE
SPIN STRUCTURE
SPIN STRUCTURE
SPIN STRUCTURE
SPIN STRUCTURE
SPIN STRUCTURE
SPIN STRUCTURE
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