amssymb} 
                \usepackage{amsbsy}
                \usepackage{mathrsfs}
                \usepackage{upgreek}
                \setlength{\oddsidemargin}{-69pt}
                \begin{document}$$h\geqslant h^*_1$$\end{document}$, have been integrated out and that after their integration the generating function has the following structure, analogous to the one at scale 0:$$\documentclass[12pt]{minimal}
                \usepackage{amsmath}
                \usepackage{wasysym} 
                \usepackage{amsfonts} 
                \usepackage{amssymb} 
                \usepackage{amsbsy}
                \usepackage{mathrsfs}
                \usepackage{upgreek}
                \setlength{\oddsidemargin}{-69pt}
                \begin{document}$$\begin{aligned} e^{ {{\mathcal {W}}}(f,A) }= \frac{e^{{{\mathcal {W}}}^{(h)}(f,A)}}{{\mathcal {N}}_h}\int P(d\Psi ^{(\leqslant h)})e^{-V^{(h)}(\Psi ^{(\leqslant h)})+B^{(h)}(\Psi ^{(\leqslant h)}, f, A)}, \end{aligned}$$\end{document}$$where $\documentclass[12pt]{minimal}
                \usepackage{amsmath}
                \usepackage{wasysym} 
                \usepackage{amsfonts} 
                \usepackage{amssymb} 
                \usepackage{amsbsy}
                \usepackage{mathrsfs}
                \usepackage{upgreek}
                \setlength{\oddsidemargin}{-69pt}
                \begin{document}$$V^{(h)}$$\end{document}$ and $\documentclass[12pt]{minimal}
                \usepackage{amsmath}
                \usepackage{wasysym} 
                \usepackage{amsfonts} 
                \usepackage{amssymb} 
                \usepackage{amsbsy}
                \usepackage{mathrsfs}
                \usepackage{upgreek}
                \setlength{\oddsidemargin}{-69pt}
                \begin{document}$$B^{(h)}$$\end{document}$ are, respectively, the effective potential and source terms, satisfying the conditions that $\documentclass[12pt]{minimal}
                \usepackage{amsmath}
                \usepackage{wasysym} 
                \usepackage{amsfonts