Formula_11563

\[\begin{gathered}\Xi=\sum_{n=0}^{\infty} \frac{z^{n}}{n !} \int d(u)_{n} \sum_{\pi} \varepsilon^{\pi} Q_{n}\left((u)_{n} ;(u)_{n}\right), \\Q_{n}=\exp \left(-\beta H_{n}^{V}\right), \\H_{n}^{V}=\left(\sum_{i=1}^{n}-\frac{\Delta_{i}}{4}+U\right)_{V^{n}}\end{gathered}\]