= Dirac-to-Weyl gamma-matrix similarity transform
{c}
{title2=$\gamma^\mu=U\widetilde\gamma^\mu U^{-1}$}
For the <Dirac representation of the gamma matrices>, the <unitary matrix>
$$
U=\frac1{\sqrt2}\begin{pmatrix}I_2&-I_2\\I_2&I_2\end{pmatrix}
$$
sends $\widetilde\gamma^0$ to $\left(\begin{smallmatrix}0&I_2\\I_2&0\end{smallmatrix}\right)$ while commuting with every spatial <gamma matrix>. This is the standard <Weyl representation of the gamma matrices> with spatial blocks $(0,\sigma^i;-\sigma^i,0)$. The <similarity transformation> preserves the <Clifford algebra> relations. Changing block-order or chirality conventions can change the displayed transformation, so its direction must be specified.
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