= Covariance of Grassmann bilinears
{title2=$\langle(\bar\theta M\theta)(\bar\theta N\theta)\rangle_c=-\operatorname{tr}(MCNC)$}
For $C=B^{-1}$, <ordered Grassmann Gaussian contractions> give $\langle\bar\theta M\theta\rangle=-\operatorname{tr}(MC)$ and $\langle(\bar\theta M\theta)(\bar\theta N\theta)\rangle=\operatorname{tr}(MC)\operatorname{tr}(NC)-\operatorname{tr}(MCNC)$. The disconnected contribution has two <fermion loops>; the connected contribution has one, giving its minus sign. This covariance is an algebraic normalized <Berezin integral>, rather than a positivity statement about a probability measure.
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