= Even-dimensional Clifford spinor dimension
{title2=$\dim_{\mathbb C}S_D=2^{D/2},\quad\dim_{\mathbb C}S_D^\pm=2^{D/2-1}$}
After complexification, pair the $D=2n$ <Clifford algebra> generators into $n$ fermionic creation and annihilation operators. Their occupation basis has $2^n$ states, giving the irreducible complex Dirac module. The chirality operator separates its even and odd occupation subspaces, each with $2^{n-1}$ states. Majorana reality conditions concern real dimensions and depend on spacetime signature; they must not be imposed in every even dimension indiscriminately.
Back to article page
