Elementary anticommutation relations

Some non-trivial commutators for elementary second-quantization operators are: \[\begin{align} & \comm{ \hat{a}^\dagger_{p \sigma} }{ \hat{a}^\dagger_{q \tau} \hat{a}_{r \mu} } = - \delta_{pr} \delta_{\sigma \mu} \hat{a}^\dagger_{q \tau} \\ % & \comm{ \hat{a}_{p \sigma} }{ \hat{a}^\dagger_{q \tau} \hat{a}_{r \mu} } = \delta_{pq} \delta_{\sigma \tau} \hat{a}^\dagger_{r \mu} \\ % & \comm{ \hat{a}^\dagger_{p \sigma} }{ \hat{a}_{q \tau} \hat{a}_{r \mu} } = \delta_{pq} \delta_{\sigma \tau} \hat{a}_{r \mu} - \delta_{pr} \delta_{\sigma \mu} \hat{a}_{q \tau} \\ % & \comm{ \hat{a}_{p \sigma} }{ \hat{a}^\dagger_{q \tau} \hat{a}^\dagger_{r \mu} } = \delta_{pq} \delta_{\sigma \tau} \hat{a}^\dagger_{r \mu} - \delta_{pr} \delta_{\sigma \mu} \hat{a}^\dagger_{q \tau} \thinspace . \end{align}\]