Spinor in a sentence

In the physics literature, abstract spinor indices are often used to denote spinors even when an abstract spinor construction is used.

In this construction a spinor can be represented as a vector of 2 k complex numbers and is denoted with spinor indices (usually α, β, γ).

Attempts at intuitive understanding The spinor can be described, in simple terms, as “vectors of a space the transformations of which are related in a particular way to rotations in physical space”.

By acting on the spinor ξ in (1), the action of Γ goes over to an action on Pythagorean triples, provided one allows for triples with possibly negative components.

In addition, sometimes the non-complexified version of Cℓ p,q (R) has a smaller real representation, the Majorana spinor representation.

In this situation, a spinor These are the right-handed Weyl spinors in two dimensions.

In this way, the spinor representations are identified with certain subspaces of the Clifford algebra itself.

It is also possible to associate a substantially similar notion of spinor to Minkowski space in which case the Lorentz transformations of special relativity play the role of rotations.

It should be strongly emphasized that this separation of the Dirac spinor into large and small components depends explicitly on a low-energy approximation.

Solutions See Dirac spinor for details of solutions to the Dirac equation.

So what precisely constitutes a "column vector" (or spinor) also depends on such arbitrary choices.

The entire Dirac spinor represents an irreducible whole, and the components we have just neglected to arrive at the Pauli theory will bring in new phenomena in the relativistic regime – antimatter and the idea of creation and annihilation of particles.

The representation shown here is known as the standard representation – in it, the wave function's upper two components go over into Pauli's 2-spinor wave function in the limit of low energies and small velocities in comparison to light.

These two inequivalent classes yield spinor transformations of opposite sign.

This is an essential feature of Dirac's theory, which ties the spinor formalism to the geometry of physical space.

This latter approach has the advantage of providing a concrete and elementary description of what a spinor is.

We then say it transforms as a spinor.