Formula_20002

\[\begin{gathered}f(p, q)=(\pi \hbar)^{-2 N} \int f_{1}\left(p_{1}, q_{1}\right) f_{2}\left(p_{2}, q_{2}\right) \times \\\quad \times \exp \left\{-\frac{2}{i \hbar}\left|\begin{array}{ccc}1 & 1 & 1 \\q_{1}, & q_{2}, & q \\p_{1}, & p_{2}, p\end{array}\right|\right\} d p_{1} d p_{2} d q_{1} d q_{2} .\end{gathered}\]