A New Perturbative Expansion for Fermionic Functional Integrals.

Abstract

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.