4-Spinors and 5D Spacetime
High Energy Physics - Theory
2013-12-10 v2 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1307.2551,
title = {4-Spinors and 5D Spacetime},
author = {Francesco Antonuccio},
journal= {arXiv preprint arXiv:1307.2551},
year = {2013}
}
Comments
10 pages. arXiv admin note: text overlap with arXiv:1206.2458