- #1
B3NR4Y
Gold Member
- 170
- 8
Homework Statement
Let
\begin{equation}
\delta _{1} \, and \, \delta _{2}
\end{equation}
be two infinitesimal sypersymmetry transformations on xμ compute
\begin{equation}
[\delta _{1}, \delta _{2} ]x^{μ}.
\end{equation}
Homework Equations
The commutator is:
\begin{equation}
[\delta _{1}, \delta _{2} ]x^{μ}=\delta_{1}\delta_{2} x^{μ} - \delta_{2}\delta_{1} x^{μ}
\end{equation}
The Attempt at a Solution
I am able to get the first term, but the second term trips me up
\begin{equation}
\begin{split}
\delta_{1}\delta_{2} &= \delta_{1}( i\bar{\epsilon}^{A}_{2} \Gamma^{μ}\theta^{A})\\
& =i\bar{\epsilon}^{A}_{2} \Gamma^{μ}\delta_{2} \theta^{A}\\
& =i\bar{\epsilon}^{A}_{2} \Gamma^{μ}\theta^{A}
\end{split}
\end{equation}