 \frac{\hbar^0}{0} \int \frac{d^D \pi}{(0 \pi \hbar)^D} \int d X^0 f^{\prime}(-\pi_{\hat 0}) \pi_{\hat k}   \operatorname{tr}[(G_0^{\rm R} - G_0^{\rm A}) \partial_{\pi_{\hat \imath}} (G_0^{{\rm R} -0} + G_0^{{\rm A} -0}) 