From c8f071589950b388fde16d0926a61410fc51766e Mon Sep 17 00:00:00 2001
From: Ian Jauslin <ian.jauslin@roma1.infn.it>
Date: Sun, 11 Sep 2016 23:42:37 +0000
Subject: Typo in definition of Fourier transform

---
 Giuliani_Jauslin_2015.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'Giuliani_Jauslin_2015.tex')

diff --git a/Giuliani_Jauslin_2015.tex b/Giuliani_Jauslin_2015.tex
index fd45555..65d8bd2 100644
--- a/Giuliani_Jauslin_2015.tex
+++ b/Giuliani_Jauslin_2015.tex
@@ -574,8 +574,8 @@ where $\mathcal H_0$ is the {\it free Hamiltonian} and $\mathcal H_I$ is the {\i
 \end{array}\label{hamx}\end{equation}
 Equation~(\ref{hamx}) can be rewritten in Fourier space as follows. We define the Fourier transform of the annihilation operators as
 \begin{equation} \hat a_{k}:=\sum_{x\in\Lambda}e^{ikx}a_{x}\;,\quad 
-\hat{\tilde b}_{k}:=\sum_{x\in\Lambda}e^{ikx}\hat{\tilde b}_{x+\delta_1}\;,\quad
-\hat{\tilde a}_{k}:=\sum_{x\in\Lambda}e^{ikx}\hat{\tilde a}_{x-\delta_1}\;,\quad
+\hat{\tilde b}_{k}:=\sum_{x\in\Lambda}e^{ikx}\tilde b_{x+\delta_1}\;,\quad
+\hat{\tilde a}_{k}:=\sum_{x\in\Lambda}e^{ikx}\tilde a_{x-\delta_1}\;,\quad
 \hat b_{k}:=\sum_{x\in\Lambda}e^{ikx}b_{x+\delta_1}\;\end{equation} 
 in terms of which
 \begin{equation}
-- 
cgit v1.2.3-54-g00ecf

