We construct a power series representation of the integrals of form \begin{equation} \text{log} \int d\mu_{S}(\psi, \bar{\psi}) \hspace{0.05 cm} e^{f(\psi, \bar{\psi}, \eta, \bar{\eta})} \nonumber \end{equation} where $\psi, \bar{\psi}$ and $\eta, \bar{\eta}$ are Grassmann variables on a finite lattice in $d \geqslant 2$. Our expansion has a local structure, is clean and provides an easy alternative to decoupling expansion and Mayer-type cluster expansions in any analysis. As an example, we show exponential decay of 2-point truncated correlation function (uniform in volume) in massive Gross-Neveu model on a unit lattice.

中文翻译：

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费米子泛函积分的新微扰展开式

我们构造了形式 \begin{equation} \text{log} \int d\mu_{S}(\psi, \bar{\psi}) \hspace{0.05 cm} e^{f 的积分的幂级数表示(\psi, \bar{\psi}, \eta, \bar{\eta})} \nonumber \end{equation} 其中 $\psi, \bar{\psi}$ 和 $\eta, \bar{\ eta}$ 是 $d \geqslant 2$ 中有限格上的 Grassmann 变量。我们的扩展具有局部结构，很干净，并且在任何分析中都可以轻松替代解耦扩展和 Mayer 型集群扩展。例如，我们展示了单位点阵上的大规模 Gross-Neveu 模型中 2 点截断相关函数（体积均匀）的指数衰减。