How to find the Majorana matrices?

[ag_swe]

I'm just wondering how the Majorana matrices first were found. I have only seen them immediately written down at different webpages, and never seen a derivation. Is it obvious how to transform the Dirac gamma matrices into the Majorana representation?

 

[PhilDSP]

This might help:

http://arxiv.org/abs/hep-th/0610252

 

[ag_swe]

Thanks, interesting paper.
In fact, since {β,α_i}=0, I think one can simply swap β and α₂, which makes all gamma matrices purely imaginary.