= Rotation and boost commutators with a fixed metric signature
{title2=$[K_i,K_j]=-si\epsilon_{ijk}J_k,\quad[J_i,K_j]=si\epsilon_{ijk}K_k$}
For the <Lorentz algebra> convention $[M_{\mu\nu},M_{\rho\sigma}]=i(M_{\mu\sigma}\eta_{\nu\rho}+M_{\nu\rho}\eta_{\mu\sigma}-M_{\mu\rho}\eta_{\nu\sigma}-M_{\nu\sigma}\eta_{\mu\rho})$, choose $\eta=\operatorname{diag}(s,-s,-s,-s)$, $s=\pm1$, $\epsilon_{123}=1$, $J_i=\epsilon_{ijk}M_{jk}/2$, and $K_i=M_{0i}$. The resulting rotation bracket is $[J_i,J_j]=si\epsilon_{ijk}J_k$ as well as the two displayed brackets. Changing the <Minkowski metric> signature while holding this generator convention fixed reverses all coefficients. A simultaneous redefinition of the generators can instead preserve the familiar form. Conventions must be specified before comparing algebra signs.
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