= Witten index
{c}
{title2=$I(\beta)=\operatorname{Tr}((-1)^F e^{-\beta H})$}
With a well-defined regulated supertrace, positive-energy states of <supersymmetric quantum mechanics> are paired by an odd invertible charge. Their opposite <fermion parities> cancel, leaving $I=n_B^0-n_F^0$, independent of $\beta$. A nonzero index proves the existence of a <supersymmetric vacuum>; zero does not prove its absence. Discrete-spectrum or suitable infrared conditions matter, because continuum thresholds and states escaping to infinity can invalidate naive trace manipulations or deformation invariance.
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