# Spinor

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## spinor

[′spin·ər]
(mathematics)
A vector with two complex components, which undergoes a unitary unimodular transformation when the three-dimensional coordinate system is rotated; it can represent the spin state of a particle of spin ½.
More generally, a spinor of order (or rank) n is an object with 2 n components which transform as products of components of n spinors of rank one.
A quantity with four complex components which transforms linearly under a Lorentz transformation in such a way that if it is a solution of the Dirac equation in the original Lorentz frame it remains a solution of the Dirac equation in the transformed frame; it is formed from two spinors (definition 1). Also known as Dirac spinor.

## Spinor

a mathematical quantity whose transformation from one coordinate system to another is governed by a special law. Spinors are used for various problems in, for example, quantum mechanics and representations of groups.

References in periodicals archive ?
Finster and Kamran propose causal fermion systems and Riemannian fermion systems as a framework describing non-smooth geometries, in particular, providing a setting for spinors on singular spaces.
In his work, the Dirac equation was extended by applying 8-dimensional spinors for the decomposition of the square root in the covariant equation of special relativity.
where [[phi].sub.L] and [[phi].sub.R] are the scalar-spinors--which are like the ordinary left and right handed Dirac spinors ([[psi].sub.L], [[psi].sub.R]); [[psi].sub.L] and [[phi].sub.R] are defined:
So, for each case of the gauge field potentials, the Rodrigues representations of upper and lower spinors and differential equations associated with them are available.
It should be noted that a formula similar to (36) may be obtained without the use of spinors. To see this, solve the zero scalar curvature equation
Penrose, R, y Rindler, W.: Spinors and Space-Time: Volume 1 y 2, TwoSpinor Calculus and Relativistic Fields.
Roth, Isometric immersions of hypersurfaces into 4-dimensional manifolds via spinors, Diff.
The space of pure spinors [Spin.sup.[+ or -]](n) is an algebraic set in projective space [P.sup.P(n)-i] that parametrizes totally isotropic subspaces of V.
Rigoli, Cartan Spinors, Minimal Surfaces and Strings II, Nuovo Cimento, 102(1988), 609-646.

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