           \begin{document}$$Z_{\rho ,\omega ,h-1}, v_{\omega ,h-1}$$\end{document}$ defined by the flow equations:$$\documentclass[12pt]{minimal}
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                \begin{document}$$\begin{aligned} Z_{\rho ,\omega ,h-1}=Z_{\rho ,\omega ,h}+z_{\rho ,\omega ,h},\qquad v_{\omega ,h-1}=v_{\omega ,h}+u_{\omega ,h}. \end{aligned}$$\end{document}$$We are now ready to integrate the fields on scale *h*. We define:$$\documentclass[12pt]{minimal}
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                \begin{document}$$\begin{aligned}&e^{-V^{(h-1)}(\Psi )+B^{(h-1)}(\Psi ,f,A)+w^{(h)}(f,A)}\nonumber \\&\quad =C_h\int {{\tilde{P}}}(d\Psi ^{(h)}) e^{-F_\xi ^{(h)}(\Psi ^{(h)}+\Psi )-F_\delta ^{(h)}(\Psi ^{(h)}+\Psi )}\times \nonumber \\&\qquad \times e^{-{{\mathcal {R}}}V^{(h)}(\Psi ^{(h)}+\Psi )+{\mathcal {L}} B^{(h)}(\Psi ^{(h)}+\Psi , f, A)+ {\mathcal {R}} B^{(h)}(\Psi ^{(h)}+\Psi , f, A)}, \end{aligned}$$\end{document}$$where $\documentclass[12pt]{minimal}
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                \begin{document}$${{\tilde{P}}}(d\Psi ^{(h)})$$\end{document}$ is the Gaussian integration with propagator $\documentclass[12pt]{minimal}
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