spinor
Sign in to savethumb|upright=1.5|A spinor visualized as a vector pointing along the Möbius band, exhibiting a sign inversion when the circle (the "physical system") is continuously rotated through a full turn of 360°.
Article
32 sectionsContents
- Introduction
- Mathematical definition
- Overview
- Representation theoretic point of view
- Geometric point of view
- Clifford algebras
- Spin groups
- Spinor fields in physics
- Spinors in representation theory
- Attempts at intuitive understanding
- History
- Examples
- Two dimensions
- Examples
- Three dimensions
- Explicit constructions
- Component spinors
- Abstract spinors
- Minimal ideals
- Exterior algebra construction
- Hermitian vector spaces and spinors
- Clebsch–Gordan decomposition
- Even dimensions
- Odd dimensions
- Consequences
- Summary in low dimensions
- Reality type and signature
- See also
- Notes
- References
- Works cited
- Further reading
thumb|upright=1.5|A spinor visualized as a vector pointing along the Möbius band, exhibiting a sign inversion when the circle (the "physical system") is continuously rotated through a full turn of 360°.
In geometry and physics, spinors (pronounced "spinner"; ) are elements of a complex vector space that can be associated with Euclidean space. Spinors can be thought of as companion geometric objects to Euclidean space that, like Euclidean vectors, respond when the Euclidean space is subjected to a rotation. A spinor transforms linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation, but unlike geometric vectors and tensors, a spinor transforms to its negative when the space rotates through 360° (see picture). It takes a rotation of 720° for a spinor to go back to its original state. Spinors are therefore often described heuristically as "square roots" of (geometric) vectors, and a geometric vector can be constructed quadratically from a spinor.