Dirac spinor


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Dirac spinor

[di′rak ′spin·ər]
(mathematics)
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The Dirac spinor can be written using the PauliDirac representation
now, let us give the corresponding lower Dirac spinor.
The lower component of Dirac spinor can be calculated by using (12) as
These two waves are a Dirac spinor satisfying the Dirac Equation.
In the latter case, the variables nj[pi] (here [pi] denotes parity and it takes the values [+ or -] 1) is an equivalent notation for a relativistic configuration because l = j [+ or -] 1/2 and the numerical parity of the l-value of a Dirac spinor upper part defines the single particle's parity.
Consider the 2-electron Coulomb interaction obtained for the upper (large) component of the Dirac spinor.
Each of these radial functions is a two-component function, one for the upper 2-component spin and the other for the lower 2-component spin that belong to a 4-component Dirac spinor.
As a matter of fact, this argument also holds for the lower pair of components of each of Dirac spinor of configuration A.
Hence by coupling the Dirac spinor dynamics to the space dynamics we derive the geodesic formalism of General Relativity as a quantum effect, but without reference to the Hilbert-Einstein equations for the induced metric.
where the solutions [phi] and [chi] for this electron-vacuum system are 2x1 Dirac spinors, and [?
the parenthetical factors implying that the operators, operating on the Dirac spinors, provide a measure of the gradients within the PV continuum.