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Gordon Decomposition
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Gordon Decomposition : ウィキペディア英語版
Gordon Decomposition
In mathematical physics, the Gordon-decomposition (named after Walter Gordon one of the discoverers of the Klein-Gordon equation) of the Dirac current is a splitting of the charge or particle-number current into a part that arises from the motion of the center of mass of the particles and a part that arises from gradients of the spin density. It makes explicit use of the of the Dirac equation and so it applies only to "on-shell" solutions of the Dirac equation.
==Original Statement==

For any solution \psi of the massive Dirac equation
: i\gamma^\mu (\nabla_\mu-m)\psi=0,
the Lorentz covariant number-current can be expressed as
:\bar\psi \gamma^\mu\psi =\frac (\bar \psi \nabla^\mu\psi -(\nabla^\mu\bar \psi) \psi)+\frac \partial_\nu(\bar\psi \Sigma^\psi),
where
:\Sigma^ = \frac ()
is the spinor generator of Lorentz transformations.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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