# Spinor

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Related to Spinor: Twistor

## 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 ?
For each potential, respectively, (6) gives the following second-order differential equations for upper spinor component:
This formula is analogous to (36) and was obtained without the use of spinors. Note that part of the integrand on the right-hand side of (40) satisfies an elliptic equation with respect to the metric g, even though the solution depends on t:
For more convinience, we will denote in the sequel all the metrics and also hermitian products on spinor bundles by the same classical notation (*, *) (no confusion is possible).
By definition, we have that the tropical pure spinor space [TSpin.sup.[+ or -]](n) is contained in the [DELTA]-Dressian [DELTA]Dr(n).
Provided a certain transformational condition is met [i.e., the condition given in equation (28) of ], it [[psi]] can be the typical Dirac spinor.
The Killing spinor equations imply that supersymmetric solutions preserve 2, 4, 6, or 8 of the supersymmetries.
This explicit solution requires the calculation of a Pauli spinor with a spatial extension.
where [psi] = [([[zeta].sub.1], [[zeta].sub.2]).sup.T] is a two component spinor and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are Pauli matrices.

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