= Energy positivity in global supersymmetry
{title2=$H=\tfrac14\sum_\alpha\{Q_\alpha,Q_\alpha^\dagger\}\ge0$}
For $\{Q_\alpha,Q_\beta^\dagger\}=2\sigma^\mu_{\alpha\dot\beta}P_\mu$, summing diagonal components gives $4H$. The expectation of each <anticommutator> is $\|Q_\alpha v\|^2+\|Q_\alpha^\dagger v\|^2$, so $H$ is a <positive semidefinite operator>. A vacuum has zero energy exactly when every <supercharge> annihilates it. Spontaneously broken global <supersymmetry> with an existing vacuum therefore gives positive <vacuum energy> density. This statement fixes the energy zero through the algebra and does not apply to the general <supergravity F-term potential>.
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