Re: I Link: Dirac Equation in 3+1 dimensions

Posted by CABrannen on October 06, 2003 at 15:18:22:

In Reply to: I Link: Dirac Equation in 3+1 dimensions posted by kx21 on October 05, 2003 at 18:04:19:

The version of the Dirac equation that I'm working with is the "chiral", which separates the spinor into right handed and left handed parts.

Part of the reason for doing this is because the weak interactions indicate that this is the way that nature is organized. The other reason is that you can eliminate the complex numbers from the couple equations in this version of the Dirac equation, other than the complexes that are embedded in the pauli spin matrices. And since Hesenes has a good geometrical version of the pauli spin matrices that eliminates the complex numbers from that, (and replaces them with numbers in the "geometrical algebra" which have geometric definitions), the result is a pair of Dirac equations that have no complex numbers.

To get the Dirac equation with no complex numbers (other than the pauli spin matrices, which are interpreted as defining a rotation in R3 and need not be explicitly written in any particular matrix form), you replace Psi_R with i Psi_R in the version of the Dirac equation that is written in the following link (about halfway down, just above the text "so that the mass term clearly mixes the left- and right-handed representations":

• Lecture 9 Appendix: Spin, helicity, handedness

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• M Physics 21: Topology of Matrix ~ Manifold of Geometry -- kx21 10/06/03 (0)

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