Dirac spinor


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Dirac spinor

[di′rak ′spin·ər]
(mathematics)
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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.
This equation shows that the Dirac spinor propagates wrt to the 3-space, and that there are dynamical effects associated with that that are not in the generalised Schrodinger equation (13).
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.
Because the complex Dirac spinor encodes both the dynamics of the electron and its anti-particle, the positron (the negative energy solutions), the vacuum-to-vacuum amplitude corresponding to the electron (positive energy solutions, propagating forward in time) must be then Z = [square root of det([gamma].
the parenthetical factors implying that the operators, operating on the Dirac spinors, provide a measure of the gradients within the PV continuum.