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It is possible to represent the Dirac matrices in the Majorana basis using $N= 2^{⌊d/2⌋}$-dimensional matrices, as shown here. This source uses a Minkowski metric. It would then be possible to move to a Euclidean metric by multiplying the time-like matrix by $i$, but then we aren't using the Majorana basis anymore. So is there a way to represent the matrices in the Majorana basis in $N= 2^{⌊d/2⌋}$ dimensions, or must we use $N= 2^{⌊(d+1)/2⌋}$?

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