diff --git a/Manuscript/SRGGW.tex b/Manuscript/SRGGW.tex
index ec6232f..11a2540 100644
--- a/Manuscript/SRGGW.tex
+++ b/Manuscript/SRGGW.tex
@@ -62,8 +62,8 @@
 
 \begin{document}	
 
-% \title{A Similarity Renormalization Group Approach To Many-Body Perturbation Theory}
-\title{Tackling The Intruder-State Problem In Many-Body Perturbation Theory: A Similarity Renormalization Group Approach/Perspective}
+\title{A similarity renormalization group approach to Green's function methods}
+%\title{Tackling The Intruder-State Problem In Many-Body Perturbation Theory: A Similarity Renormalization Group Approach/Perspective}
 
 \author{Antoine \surname{Marie}}
 	\email{amarie@irsamc.ups-tlse.fr}
@@ -74,7 +74,12 @@
 	\affiliation{\LCPQ}
 
 \begin{abstract}
-Here comes the abstract.
+The family of Green's function methods based on the $GW$ approximation has gained popularity in the electronic structure theory thanks to its accuracy in weakly correlated systems and its affordability.
+Despite this, self-consistent versions still pose challenges in terms of convergence.
+A recent study \href{https://doi.org/10.1063/5.0089317}{[J. Chem. Phys. 156, 231101 (2022)]} has linked these convergence issues to the intruder-state problem.
+In this work, a perturbative analysis of the similarity renormalization group (SRG) approach is performed on Green's function methods.
+The resulting SRG-based regularized self-energy significantly accelerates the convergence of self-consistent $GW$ methods. 
+Furthermore, it enables us to derive, from first principles, the expression of a new naturally Hermitian form of the static self-energy that can be employed in quasiparticle self-consistent $GW$ (qs$GW$) calculations.
 %\bigskip
 %\begin{center}
 %	\boxed{\includegraphics[width=0.5\linewidth]{TOC}}
@@ -101,7 +106,6 @@ The $GW$ method approximates the self-energy $\Sigma$ which relates the exact in
 \end{equation}
 where $1 = (\bx_1, t_1)$ is a composite coordinate gathering spin-space and time variables.
 The self-energy encapsulates all the Hartree-exchange-correlation effects which are not taken into account in the reference system.
-%Throughout this manuscript the references are chosen to be the Hartree-Fock (HF) ones so that the self-energy only account for the missing correlation.
 Approximating $\Sigma$ as the first-order term of its perturbative expansion with respect to the screened Coulomb potential $W$ yields the so-called $GW$ approximation \cite{Hedin_1965,Martin_2016}
 \begin{equation}
   \label{eq:gw_selfenergy}
@@ -535,7 +539,7 @@ This transformation is done gradually starting from the states that have the lar
   \centering
   \includegraphics[width=\linewidth]{fig1.pdf}
   \caption{
-    Add caption
+    Functional form of the qs$GW$ self-energy (left) for $\eta = 1$ and the SRG-$GW$ self-energy (right) for $s = 1/(2\eta^2)$.
     \label{fig:fig1}}
 \end{figure*}
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