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1. Spinors in three dimensions: 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. This is part of the detailed algebraic discussion of the rotation group SO(3). (Spin representations of the SO(3) group) [100%] 2026-06-14 [Linear algebra] [Spinors]...

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1. Spinor: In geometry and physics, spinors /spɪnər/ are elements of a complex number-based vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation, but unlike geometric ... (Non-tensorial representation of the spin group) [100%] 2023-12-22 [Spinors] [Rotation in three dimensions]...
2. Spinor: An element of a spinor representation space. For example, if $Q$ is a non-degenerate quadratic form on an $n$-dimensional space $V$ over a field $k$ with maximal Witt index $m=[n/2]$ (the latter condition always holds when ... (Mathematics) [100%] 2023-11-28
3. Spinor: In geometry and physics, spinors /spɪnər/ are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight (infinitesimal ... (Physics) [100%] 2023-01-16 [Spinors] [Rotation in three dimensions]...
4. Spinor structure: on an $ n $- dimensional manifold $ M $, fibration of spin-frames A principal fibre bundle $ \widetilde \pi : \widetilde{P} \rightarrow M $ over $ M $ with structure group $ \mathop{\rm Spin} _ {n} $( see Spinor group), covering some principal fibre bundle $ \pi : P ... (Mathematics) [70%] 2024-01-12
5. Spinor representation: spin representation The simplest faithful linear representation (cf. Faithful representation; Linear representation) of the spinor group $ \mathop{\rm Spin} _ {n} ( Q) $, or the linear representation of the corresponding even Clifford algebra $ C ^ {+} = C ^ {+} ( Q) $( see Spinor group; $ Q $ is ... (Mathematics) [70%] 2023-10-18
6. Spinor group: The spinor group or spin group is associated to a non-degenerate quadratic form $Q$ on an $n$-dimensional vector space $V$ ($n\ge 3$) over a field $k$. It is a connected linear algebraic group which is the simply ... (Mathematics) [70%] 2023-10-12
7. Spinor condensate: Spinor condensates are degenerate Bose gases that have degrees of freedom arising from the internal spin of the constituent particles . They are described by a multi-component (spinor) order parameter. (Physics) [70%] 2022-12-07 [Bose–Einstein condensates] [Exotic matter]...
8. Spinor condensate: Spinor condensates are degenerate Bose gases that have degrees of freedom arising from the internal spin of the constituent particles . They are described by a multi-component (spinor) order parameter. [70%] 2024-01-03 [Bose–Einstein condensates] [Exotic matter]...
9. Spinor bundle: In differential geometry, given a spin structure on an \displaystyle{ n }[/math]-dimensional orientable Riemannian manifold \displaystyle{ (M, g),\, }[/math] one defines the spinor bundle to be the complex vector bundle \displaystyle{ \pi_{\mathbf S}\colon{\mathbf S}\to M ... [70%] 2023-12-23 [Algebraic topology] [Riemannian geometry]...
10. Spinor field: In differential geometry, given a spin structure on an n-dimensional orientable Riemannian manifold (M, g), a section of the spinor bundle S is called a spinor field. A spinor bundle is the complex vector bundle \displaystyle{ \pi_{\mathbf S ... (Physics) [70%] 2023-12-29 [Riemannian geometry] [Structures on manifolds]...