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 ?
The Dirac conjugate [degrees][PSI] of the plane wave spinor (6)bis is here:
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).
5 If n [less than or equal to] 5 then the tropical pure spinor space [TSpin.
Following from this viewpoint is the concept that the 2x1 spinors [phi] and [chi] represent, respectively, the PV response to the electron core (-[e.
Depending on the type of the representation of the spinor group Spin(n),we define h to be m - 1 or m in Table I.
The continuous rotation and reversal of the inward wave amplitude at the center is expressible in Dirac's spinor algebra.
The spinor field that is the hermitian conjugate of [psi] is the 1x4 row vector [[psi].
The implementation of the pure spinor constraint is as an Abelian gauge symmetry, where the generators ([lambda][[gamma].
But although Dirac's equation is Lorentz-covariant, his state-function is a 4x1 matrix which behaves, not like a 4-vector, but like a spinor whose transformation is fixed by a change of frame only to within a factor of [+ or -]1.
mu]]u(p) where spinor states u(p) include the helicity states.
The authors have organized the main body of their text in eighteen chapters devoted to the early history of spin, the quantum mechanics of spin, the bloch sphere, the evolution of a spinor on the bloch sphere, and a wide variety of other related subjects.