Formula_12776

\[\begin{gathered}f=\left\{f_{s}^{B}\left(\overrightarrow{q_{1}}, \overrightarrow{p_{1}} ; \ldots ; \overrightarrow{q_{s}}, \overrightarrow{p_{s}}\right), s=0,1,2, \ldots, N\right\}, \\f_{s}^{B}\left(\overrightarrow{q_{1}}, \overrightarrow{p_{1}} ; \ldots ; \vec{q}_{s}, \overrightarrow{p_{s}}\right)=\left(8 \pi^{3}\right)^{-s} \int d \overrightarrow{k_{1}} \ldots d \overrightarrow{k_{s}} \times \\\times \exp \left(-i \sum_{n=1}^{s} \overrightarrow{k_{n}} \overrightarrow{p_{n}}\right) \operatorname{Tr}\left(\rho \Psi^{+}\left(\overrightarrow{q_{1}}-\frac{\hbar}{2} \overrightarrow{k_{1}}\right) \ldots \Psi^{+}\left(\overrightarrow{q_{s}}-\frac{\hbar}{2} \overrightarrow{k_{s}}\right) \times\right. \\\left.\times \Psi\left(\overrightarrow{q_{s}}+\frac{\hbar}{2} \overrightarrow{k_{s}}\right) \ldots \Psi\left(\overrightarrow{q_{1}}+\frac{\hbar}{2} \overrightarrow{k_{1}}\right)\right),\end{gathered}\]