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| -rw-r--r-- | frsb_kac-rice.tex | 20 |
1 files changed, 12 insertions, 8 deletions
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index 1a33581..2f1a55e 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} |