In the context of the Dirac equation and Weyl equation, the Weyl spinors satisfying the Weyl equation transform under the simplest irreducible spin representations of the Lorentz group, since the spin quantum number in this case is the smallest non-zero number allowed: 1/2. The 2-component left-handed Weyl spinor transforms under D and the 2-component right-handed Weyl spinor transforms under D. Dirac spinors satisfying the Dirac equation transform under the representation D ⊕ D, the direct sum of the irreps for the Weyl spinors.