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Yingjie Wang
2026-04-09 22:25:18 -04:00
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\end{frame} \end{frame}
\begin{frame}{Towards first order Z4c}{First order reduction} \begin{frame}{Towards first order Z4c}{First order reduction}
\subsection{First order reduction: wave equation} \subsection{First order reduction: wave equation as an example}
We can introduce auxiliary variables to reduce a second order PDE system to a first order one. For example, for the wave equation on flat spacetime: We can introduce auxiliary variables to reduce a second order PDE system to a first order one. For example, for the wave equation on flat spacetime:
\begin{equation} \begin{equation}
\Partial{t}^2 {\phi} - \tensor{\delta}{^i^j} \Partial{i} \Partial{j} \phi = 0, \Partial{t}^2 {\phi} - \tensor{\delta}{^i^j} \Partial{i} \Partial{j} \phi = 0,