 \int_{\Omega} d{\mbox{\boldmath $X$}}\langle \; {\mbox{\boldmath $x$}}, {\mbox{\boldmath $X$}}\mid ((\hat{\rho}(t)\star\hat{G}) \star \hat{{\mbox{\boldmath $v$}}}) \mid {\mbox{\boldmath $x$}}, {\mbox{\boldmath $X$}}\; \rangle 