From 8cf1d620d86f738f2b209ea3e9694b96338335e1 Mon Sep 17 00:00:00 2001
From: "kurchan.jorge" <kurchan.jorge@gmail.com>
Date: Sun, 5 Jun 2022 13:21:46 +0000
Subject: Update on Overleaf.

---
 frsb_kac-rice.tex | 20 ++++++++++++--------
 1 file changed, 12 insertions(+), 8 deletions(-)

(limited to 'frsb_kac-rice.tex')

diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index ca87ee5..c9c9ce8 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -431,7 +431,16 @@ The second equation implies
 
 \subsection{Motivation}
 
-The reader who is happy with the ansatz may skip this section. 
+We shall make the following ansatz
+to putting:
+\begin{eqnarray}
+Q_{ab}&=& {\mbox{ a Parisi matrix}}\nonumber\\
+R_{ab}&=&R_d \delta_{ab}&\nonumber\\
+D_{ab}&=& D_d \delta_{ab}\label{ansatz}
+\end{eqnarray}
+This ansatz closes under the operations that are involved in the replicated action.
+The reader who is happy with the ansatz may skip the rest of this section.
+
  We may encode the original variables in a superspace variable:
 \begin{equation}
   \phi_a(1)= s_a + \bar\eta_a\theta_1+\bar\theta_1\eta_a +  \hat s_a \bar \theta_1 \theta_1
@@ -466,13 +475,8 @@ The odd and even fermion numbers decouple, so we can neglect all odd terms in $\
 The variables $\bar \theta \theta$ and $\bar \theta ' \theta'$ play
 the role of `times' in a superspace treatment. We have a long experience of
 making an ansatz for replicated quantum problems, which naturally involve a (Matsubara) time. The analogy strongly
-suggests that only the diagonal ${\bf Q}_{aa}$ depend on the $\theta$'s. This boils down
-to putting:
-\begin{eqnarray}
-Q_{ab}&=& {\mbox{ a Parisi matrix}}\nonumber\\
-R_{ab}&=R_d \delta_{ab}&\nonumber\\
-D_{ab}&=& D_d \delta_{ab}
-\end{eqnarray}
+suggests that only the diagonal ${\bf Q}_{aa}$ depend on the $\theta$'s. This boils down the ansatz \ref{ansatz}
+
 Not surprisingly, this ansatz closes, as we shall see. That it closes under Hadamard products is simple.
 
 \begin{equation}
-- 
cgit v1.2.3-70-g09d2

