= Trace normalization of su(2)
{title2=$e_a=-i\sigma_a/\sqrt2,\quad[e_a,e_b]=\sqrt2\varepsilon_{abc}e_c$}
With the defining two-dimensional <matrix trace> and <inner product> $\langle X,Y\rangle=-\operatorname{tr}(XY)$, the displayed <Pauli matrix> basis is orthonormal. The <Pauli matrix multiplication law> gives the indicated <structure constants of a Lie algebra>. With the alternative form $-2\operatorname{tr}(XY)$, the orthonormal basis is $-i\sigma_a/2$ and the structure constant is one. The bracket and inner-product normalizations must be kept consistent in projected gauge-field formulas.
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