Dirac Spinor: 4 component object that transforms under boost and rotations according to a Ki, Ji matrices.
The most important finite dimensional almost irreducible rep of L+ is the
dirac spinor.
if {Gu,Gn}=anticommutator=-2nuv (a dirac algebra) => Sun=i/4[Gu,Gn].
Gu's are 4x4 matrices.
G0=
O I2
I2 0
Gi=
0 Si
-Si 0
Ki=S0i=i/4*[G0,Gi]= -i/2*
Si 0
0 -Si
Ji= .5*eijk Sjk= .5*
Si 0
0 Si