= Mostly-plus Dirac propagator with a real derivative kernel
{title2=$\langle T\psi\bar\psi\rangle(p)=i(-i\gamma\cdot p+m)/(-p^2-m^2+i0)$}
For action $-\int\bar\psi(\gamma\cdot\partial+m)\psi$, choose <gamma matrices> with $\{\gamma^\mu,\gamma^\nu\}=2\eta^{\mu\nu}$ and signature $(-,+,\ldots,+)$. The Fourier kernel of $D=\gamma\cdot\partial+m$ is $i\gamma\cdot p+m$. Its algebraic inverse is $(-i\gamma\cdot p+m)/(p^2+m^2)$. The <Grassmann Gaussian integral> for $e^{-i\bar\psi D\psi}$ has covariance $-iD_F^{-1}$, giving the displayed <Dirac propagator>. Its denominator has positive-energy poles below and negative-energy poles above the real energy axis by the <Feynman i-epsilon prescription>. Both the metric and the factor of $i$ in the derivative kernel must be specified when comparing propagator formulas.
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