= Hermitian quantum generator convention
{c}
{title2=$H_X=i\rho(X)$}
For a unitary derived representation $\rho$, its generators are anti-Hermitian. Define Hermitian observables $H_X=i\rho(X)$; then their ordinary operator <commutator> is $[H_X,H_Y]=iH_{[X,Y]}$. Thus real <Lie algebra> structure constants and Hermitian-operator commutation relations differ by an $i$. Products in a <universal enveloping algebra> require one conversion factor for every generator. In particular, the abstract bilinear Pauli-Lubanski element has representation image minus the pseudovector formed from the Hermitian physical generators.
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