= BPS bound in supersymmetry
{c}
{title2=$M\ge\frac12\max_r|Z_r|$}
Use $\{Q^A_\alpha,Q^B_\beta\}=\epsilon_{\alpha\beta}Z^{AB}$. <Unitary skew-diagonalization of an antisymmetric matrix> gives two-by-two blocks with entries $Z_r=2z_r$. At rest, the paired <supercharges> have <anticommutators> $2(M\pm|z_r|)$. The squared <norms> of an operator and its adjoint sum to the expectation of their <anticommutator>, so positive <norm> requires $M\ge|z_r|$ for every block. A convention with $2Z$ in the algebra instead writes $M\ge\max|Z_r|$.
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