update: auto commit

report.tex

@@ -316,7 +316,15 @@
   \end{frame}
 
   \begin{frame}{Towards first order Z4c}{constraints during the reduction}
-    For example, we can add a constraint damping term $-\gamma \mathcal{C}_i$ to the evolution equation of $\tensor{\psi}{_i}$, where $\gamma > 0$ is a constant. Then the evolution of the constraints becomes
+    For example, we can add a constraint damping term $-\gamma \mathcal{C}_i$ to the evolution equation of $\tensor{\psi}{_i}$,
+    \begin{equation}
+      \begin{cases}
+        \Partial{t}{\phi} = \pi, \\
+        \Partial{t}{\pi} = \tensor{\delta}{^i^j} \Partial{i} \tensor{\psi}{_j},\\
+        \Partial{t}{\tensor{\psi}{_i}} = \Partial{i} \pi - \gamma \mathcal{C}_i,
+      \end{cases}
+    \end{equation}
+    where $\gamma > 0$ is a constant. Then the evolution of the constraints becomes
     \begin{equation}
       \Partial{t} \mathcal{C}_i = -\gamma \mathcal{C}_i,
     \end{equation}