Formula_14565

\[\begin{gathered}(P \pi)\left(\xi_{1}, \ldots, \xi_{s} ;\left[\Gamma_{s}\right]\right)=\int d k_{1}^{\prime} \ldots d k_{s}^{\prime} \times \\\times\left\langle k_{1}, \ldots, k_{s}\left|P_{s}\left(\Gamma_{s}\right)\right| k_{1}^{\prime}, \ldots, k_{s}^{\prime}\right) \pi_{s}\left(k_{1}^{\prime}, p_{1} ; \ldots ; k_{s}^{\prime}, p_{s} ;\left[\Gamma_{s}\right]\right), \\P_{s}\left(\Gamma_{s}\right)=\sum_{\left(\Gamma_{s}\right)}(-1)^{P} \delta\left[-k_{1}^{\prime}+\frac{1}{\hbar}\left(p_{i_{1}}-p_{1}\right)+\frac{1}{2}\left(k_{i_{1}}+k_{1}\right)\right] \ldots \times \\\times \delta\left[-k_{s}^{\prime}+\frac{1}{\hbar}\left(p_{i_{s}}-p_{s}\right)+\frac{1}{2}\left(k_{i_{s}}+k_{s}\right)\right] \times \\\times \exp \left[\frac{\hbar}{2} \sum_{n=1}^{s}\left(k_{n}^{\prime}-k_{n}\right) \frac{\partial}{\partial p_{n}}\right]\end{gathered}\]