Most recent edit on 2008-02-13 23:24:42 by CharlesFrancis

Additions:
where p satisfies the mass shell condition and u is a Dirac spinor» having the form, for r = 1, 2, and for a two-spinor ζ normalised so that

Deletions:
where p satisfies the mass shell condition and u is a Dirac spinor» having the form, for r = 1, 2, and for a two-spinor ζ normalised so that

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Edited on 2008-01-08 03:40:48 by CharlesFrancis

Additions:

Deletions:

Proof:

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Oldest known version of this page was edited on 2008-01-08 03:16:45 by CharlesFrancis []

Solution of the Dirac Equation

The positive energy solutions to the Dirac equation are
where p satisfies the mass shell condition and u is a Dirac spinor» having the form, for r = 1, 2, and for a two-spinor ζ normalised so that
Proof:
Proof: Observe that
So,


Hence,





Then, differentiation of the solution of the Dirac equation gives,
as required.

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Normalisation of Dirac Spinors

The Pauli spin matrices are Hermition, so (as above)
Then

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