Ian Jauslin
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authorIan Jauslin <ian.jauslin@roma1.infn.it>2016-09-11 23:42:37 +0000
committerIan Jauslin <ian.jauslin@roma1.infn.it>2016-09-11 23:42:37 +0000
commitc8f071589950b388fde16d0926a61410fc51766e (patch)
tree76be50fea1fb1ef614be5194f3a6e18cb7cb7e62
parent242a8e123d473e1f255288e0f03dcbb608d907fc (diff)
Typo in definition of Fourier transformHEADv1.0.1master
-rw-r--r--Giuliani_Jauslin_2015.tex4
1 files changed, 2 insertions, 2 deletions
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}