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 ?
a] is the Dirac operator and it is customary to omit the spinor indices A, B by simply writing [[gamma].
Then, we will give some facts about restrictions of spinors on a surface into a 4-dimensional space and deduce the particular spinor fields with which we will work in the sequel.
By definition, we have that the tropical pure spinor space [TSpin.
where the solutions [phi] and [chi] for this electron-vacuum system are 2x1 Dirac spinors, and [?
Let us recall complex representation rings of spinor groups.
His theoretical spinor algebra produced correct values of the electron's energy and spin but gave no hint of the physical structure of the electron.
Spinor Bose-Einstein condensates (BECs) are highly controllable ultracold atom systems whose internal (spin) degree of freedom allows for different types of magnetic ordering, therefore offering a wider span of magnetic quantum phases.
The Dirac equation that defines the free-electron spinor field [psi] = [psi](r, t) [1, p.
They cover basic spinorial material, lowest eigenvalues of the Dirac operator on closed spin manifolds, special spinor field and geometries, and Dirac spectra of model spaces.
A reduction of the full two dimensional evolutionary spinor Ginzburg-Landau model can be made which leads to a simplified model that retains the basic features ([1], [8], [9]), related to the superconductivity model introduced in [7]:
Pure spinor superfields were developed with the purpose of covariant quantization of superstrings by Berkovits [4-7] and the cohomological structure was independently discovered in supersymmetric field theory and supergravity, originally in the context of higher-derivative deformations [8-17].