So we have the rules for creation and annihilation operators.
\begin{equation} \left[ a_\textbf{p}, a_\textbf{q}^\dagger \right] = \delta_{\textbf{p},\textbf{q}} \end{equation} and \begin{equation} \left[ a_\textbf{p}, a_\textbf{q} \right] = \left[ a^\dagger_\textbf{p}, a_\textbf{q}^\dagger \right] = 0 \end{equation}
I just have the question, does this mean that \begin{equation} \left[ a_\textbf{p}, a_\textbf{-p}^\dagger \right] = 0 \end{equation}
Despite having the same momentum just, in the opposite direction?
What if I was to apply the creation operator $a^\dagger_\textbf{-p}$ on the state $\left|n, \textbf{p} \right>$?
If the commutator does equal zero, is this an example of right handed and left handed particles (opposite helicity) not interacting?
Thank you for reading.