In the lectures of Gary Gibbons on Supergravity held 2009@DAMTP http://www.damtp.cam.ac.uk/research/gr/members/gibbons/gwgPartIII_Supergravity.pdf it is remarkable that when he introduces spinors he avoids systematically the use of the imaginary $i$. So he presents the Dirac-equation in Majorana presentation and chooses to describe Dirac-spinors (bispinors) as a pair of Majorana spinors. Why does he make such a choice ? Are complex numbers are incompatible with gravity respectively Supergravity ? I guess, it is some kind of related with the compromitted unitarity in gravity, but the lectures don't tell nothing particular on it. Does missing unitarity mean that the use of complex numbers does not make sense ? Does anybody know more about it and can explain it ?