# 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 ?
Following from this viewpoint is the concept that the 2x1 spinors [phi] and [chi] represent, respectively, the PV response to the electron core (-[e.
Roth, Isometric immersions of hypersurfaces into 4-dimensional manifolds via spinors, Diff.
P(n)] is the tropicalization of the space of pure spinors, i.
Now we shall see below that the IN- and OUT-wave pairs of the WSM are real physical spinors, the counterpart of Dirac's theoretical spinors.
This solution was re-presented using a variety of alternative mathematical tools, from the more familiar spinors to Pfaffians and quasi-particles, the latter signalling a return to the algebraic approach.
Therefore, says Hestenes, it is well qualified to handle the many directed quantities in physics in a very natural way, including the complicated ones called spinors, which other mathematical languages that have been used cannot handle.
It is suggested to use split octonions as universal mathematical structure in physics, instead of vectors, tensors, spinors, etc.
Written for students and others interested in theoretical physics, this presents the fundamental principles of the electroweak, the gluons and the gravity gauge theories obtained from the probability of physics events formulated by the spinors.
The general way to include spinors in spacetime is to use a nonholonomic tetrad structure and keep the algebra the same in each such defined space.

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