Wednesday, July 10, 2013

1307.2551 (Francesco Antonuccio)

4-Spinors and 5D Spacetime    [PDF]

Francesco Antonuccio
We revisit the subject exploring maps from the space of 4-spinors to 3+1 space-time that commute with the Lorentz transformation. All known mappings have a natural embedding in a higher five dimensional spacetime, and can be succinctly expressed as products of quaternions, or split-quaternions, depending on the signature of the embedding 5D spacetime. It is in this sense that we may view the geometry of 4-spinors as being related to the `square root' of five dimensional spacetime. In particular, a point in 5D spacetime may be identified with a corresponding 4-spinor that is uniquely determined up to a quaternionic - or split-quaternionic - phase.
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