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 ?
0] factor in the Dirac representation where we assume the amplitude for the resting positron is chosen in the "v" component of the spinor [psi] = ([?
5 If n [less than or equal to] 5 then the tropical pure spinor space [TSpin.
For example, inverting a spin state is produced by the inversion matrix operating on the spinor,
Then the scalar (ghost number 1, dimension 0) in the first column is interpreted as the Yang-Mills ghost and the vector and spinor in the second column are interpreted as the fields of the super-Yang-Mills multiplet (the field [[psi].
This zero spinor indicates that the mass energy of the free particle is being ignored, while the effective negative-mass energy of the "vacuum particle" has been doubled.
Consider the 2-electron Coulomb interaction obtained for the upper (large) component of the Dirac spinor.
4] called the right-handed spinor representation [S.
As a matter of fact, this argument also holds for the lower pair of components of each of Dirac spinor of configuration A.
With respect to the SM, Sivaram [6] indicates that the Dirac spinor can gain mass via a strong gravity field.
It can also be mentioned here that spinor SL(2,C) representation of GTR has been discussed in standard textbooks on General Relativity, see for instance Wald (1983).