= Solution
Use dimensionless physical <helicity> $h=\mathbf S\cdot\hat{\mathbf p}$, with <spin> <eigenvalues> $\pm1/2$ in <natural units>. In the <Dirac representation of the gamma matrices>[Dirac representation],
$$
\boxed{h_D=\frac12\begin{pmatrix}\boldsymbol\sigma\cdot\hat{\mathbf p}&0\\0&\boldsymbol\sigma\cdot\hat{\mathbf p}\end{pmatrix}.}
$$
The entries $1$ in the supplied transformation denote two-by-two <Identity matrix>[identities]. Since its <matrix> acts only on the upper/lower <spinor> blocks, it <Commuting operators>[commutes] with the repeated <Pauli matrices>[Pauli block]. Therefore $u^{-1}=u$ and
$$
\boxed{h_W=u h_Du^{-1}=h_D.}
$$
The <eigenvalues> remain the physical <Spin>[spin projection] along the direction of motion, $+1/2$ or $-1/2$. A convention omitting the factor one half instead labels them $\pm1$; this changes no measurement <probabilities>. A change of <Gamma matrices>[gamma-matrix representation] cannot change the <spin> observable.
Back to article page
