TFPT scientific source excerpt
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000001 | \subsection{Renormalized, physical, and scheme readout layers}
000002 | 
000003 | \begin{definition}[Admissible effective average action]
000004 | \label{def:admissible-effective-average-action}
000005 | Let $R_k$ be an admissible infrared regulator commuting with the structural sector selection.
000006 | Define
000007 | \[
000008 | e^{W_k[J]}
000009 | :=
000010 | \int_{\mathcal H_{\mathrm{adm}}}\mathcal D\varphi\,
000011 | \exp\!\Bigl(
000012 | -S_{\mathrm{adm}}[\varphi]
000013 | -\frac12\langle \varphi,R_k\varphi\rangle
000014 | +\langle J,\varphi\rangle
000015 | \Bigr),
000016 | \]
000017 | and set
000018 | \[
000019 | \Gamma_k[\phi]
000020 | :=
000021 | \sup_J\{\langle J,\phi\rangle-W_k[J]\}
000022 | -\frac12\langle \phi,R_k\phi\rangle.
000023 | \]
000024 | The renormalized admissible effective action is
000025 | \[