In the Dirac representation, the most convenient definitions for the two-spinors are: ϕ ϕ 1 = [ 1 0 ] ϕ ϕ 2 = [ 0 1 ] and χ χ 1 = [ 0 1 ] χ χ 2 = [ 1 0 ] since these form an orthonormal basis with respect to a (complex) inner product.