It is a common belief among theoretical physicists that the charge conjugation of the Dirac equation has an analogy in higher dimensional space-times so that in an 8-dimensional space-time there would also be Maiorana spinors as eigenspinors of a charge conjugation, which would swap the sign of the electric charge of the Dirac equation. This article shows that this mistaken belief is based on inadequate distinction between two kinds of charge conjugation: the electric conjugation swapping the sign of the Dirac equation and the Maiorana conjugation fixing the real subalgebra (of the complexification of the Clifford algebra of the space-time). Only the latter conjugation has Maiorana spinors as its eigenspinors.
@article{bwmeta1.element.bwnjournal-article-bcpv37i1p289bwm,
author = {Lounesto, Pertti},
title = {Charge conjugation and Maiorana spinors in dimension 8},
journal = {Banach Center Publications},
volume = {37},
year = {1996},
pages = {289-293},
zbl = {1010.81506},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv37i1p289bwm}
}
Lounesto, Pertti. Charge conjugation and Maiorana spinors in dimension 8. Banach Center Publications, Tome 37 (1996) pp. 289-293. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv37i1p289bwm/
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