Page "Spinor" Paragraph 9

The most typical type of spinor, the Dirac spinor, is an element of the fundamental representation of the complexified Clifford algebra, into which the spin group Spin ( p, q ) may be embedded.

On a 2k-or 2k + 1-dimensional space a Dirac spinor may be represented as a vector of 2 < sup > k </ sup > complex numbers.

( See Special unitary group.

) In even dimensions, this representation is reducible when taken as a representation of and may be decomposed into two: the left-handed and right-handed Weyl spinor representations.

In addition, sometimes the non-complexified version of has a smaller real representation, the Majorana spinor representation.

If this happens in an even dimension, the Majorana spinor representation will sometimes decompose into two Majorana – Weyl spinor representations.