<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[12pt]{article}
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\begin{document}

\section{Functions}\label{sec4}
\DIFdelbegin %DIFDELCMD &lt; \begin{equation*}
%DIFDELCMD &lt; %%%
\DIFdelend \DIFaddbegin \begin{equation}
\DIFaddend \label{propak}
C_{b,\mu\nu}(k)\ \dot{=} 
\DIFdelbegin %DIFDELCMD &lt; \end{equation*}
\end{equation}%DIFAUXCMD
%DIFDELCMD &lt; %%%
\DIFdel{We choose a cutoff function
$\sigma_\Lambda(k^2)$:
}\begin{align*}%DIFAUXCMD
%DIFDELCMD &lt; \begin{eqnarray*}
%DIFDELCMD &lt; %%%
\DIFdel{\sigma_\Lambda(k^2)
}
\end{align*}%DIFAUXCMD
%DIFDELCMD &lt; \end{eqnarray*}
%DIFDELCMD &lt; %%%
%DIF &lt; in such a way that
%DIF &lt; \begin{eqnarray*}
%DIF &lt; \frac{d}{dk^2}\sigma_{\Lambda}(k^2=0)=0\ ,
%DIF &lt; \end{eqnarray*}
%DIF &lt; for $\Lambda&gt;0$, 
\DIFdel{and define
}%DIFDELCMD &lt; \begin{eqnarray*}
\begin{align*}%DIFAUXCMD
%DIFDELCMD &lt; %%%
\DIFdel{\sigma}\DIFdelend \DIFaddbegin \end{equation}
\DIFadd{We define the cutoff function
}\begin{eqnarray}\label{siLa0La}
\DIFadd{\sigma}\DIFaddend _{\Lambda,\Lambda_0}(k^2)\ \dot{=} \ \sigma_{\Lambda_0}(k^2)-\sigma_{\Lambda}(k^2)\ ,
\DIFdelbegin %DIFDELCMD &lt; \end{eqnarray*}
\end{eqnarray}%DIFAUXCMD
%DIFDELCMD &lt; %%%
\DIFdel{with ...
 }\begin{eqnarray}%DIFAUXCMD
\DIFdelend \DIFaddbegin \end{eqnarray}
\DIFadd{where
}\begin{eqnarray}\label{siLa}
\DIFadd{\sigma_\Lambda(k^2)
}\end{eqnarray}
 \DIFaddend\end{document}</pre></body></html>