Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Thursday, March 20, 2008

The Dirac Code IV

On extending Rowlands' quaternion units to the seven octonions of the Fano plane, one encounters a 3 Time interpretation, accounting for the three generations via the projected hexagon, as usual. Whereas Rowlands finds 4 choices of sign in the 3 quaternion terms, resulting in a 4 component state, in the octonion case, leaving 3 positive mass terms, there are $2^{4} = 16$ sign choices. But the Fano plane relations suggest a reduction of these degrees of freedom, perhaps to the 12 expected for 3 generations.

It would be interesting to combine this octonionic framework with related $E8$ ideas, although classical groups are not of particular interest in M Theory, except in establishing links with other formalisms.


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