反対称化記号の実験

\begin{align}
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa a^{{x}{q}} + b^{y} &= c^{z} + d^{w} \quad\text{($x=y$のとき)}\label{a}\\[15pt]
p^{x} + q^{y} &= r^{z} + t^{w} \\
m^{i} + n^{j} &= o^{k} + t^{l}\\
D^{\mu_1} + E^{q} &= F^{r} \quad \text{markerA}
\end{align}

\begin{equation}
\begin{split}
\notag\\[2pt]
\gamma_{\mu_1 \mu_2\cdots \mu_k}\gamma_{\nu_1 \nu_2\cdots \nu_l}
=\sum_{m=0}^{\min(k,l)}(-1)^{\frac{1}{2}m\qty(2k-m-1)}\frac{k! l!}{(k-m)! (l-m)! m!}\eta_{{\mu_1}{\nu_1}}\eta_{{\mu_2}{\nu_2}}\cdots\eta_{{\mu_m}{\nu_m}}\gamma_{{\mu_{m+1}}\cdots {{\mu_k}}{\nu_{m+1}}\cdots{\nu_l}} \notag \\[5pt]
D^{\mu_1} + E^{q} &= F^{r}\label{1}
\end{split}
\end{equation}

\begin{align}
(-1)^{\frac{1}{2}m\qty(2k-m-1)}\frac{k! l!}{(k-m)! (l-m)! m!}i^{\frac{s-t-1}{2}}\tr\qty[\gamma_*]\delta^{\mu_1}_{\nu_1}\delta^{\mu_2}_{\nu_2}\cdots\delta^{\mu_m}_{\nu_m}\varepsilon^{{\mu_{m+1}}{\mu_{m+2}}\cdots{\mu_k}}_{\hspace{70pt}{\nu_{m+1}}{\nu_{m+2}}\cdots{\nu_l}}
\end{align}

\begin{align}
A_{\mu_1}B_{\mu_2}\qty(C_{\mu_3})=A^{p}B^{q}\qty(C^{r})
\end{align}

\begin{align}
X=
\begin{cases}
A^{\mu_1}D^{\mu_2}E^{\mu_3}C^{\mu_4}\\[15pt]
X_{x}Y_{y}Z_{z}
\end{cases}
\end{align}