- #1
Luca_Mantani
- 36
- 1
Hi,
I was calculating some amplitudes and I end up with an expression like this:
$$(\bar{c}\gamma^\mu\gamma^\nu\gamma^\rho P_L b)(\bar{d}\gamma_\mu\gamma_\nu\gamma_\rho P_L u)$$
In the solution of the exercise they say that, from the Fierz identity:
$$(\bar{c}\gamma^\mu\gamma^\nu\gamma^\rho P_L b)(\bar{d}\gamma_\mu\gamma_\nu\gamma_\rho P_Lu)=16(\bar{c}\gamma^\mu P_L b)(\bar{d}\gamma_\mu P_L u)$$
How can I show that?
I was calculating some amplitudes and I end up with an expression like this:
$$(\bar{c}\gamma^\mu\gamma^\nu\gamma^\rho P_L b)(\bar{d}\gamma_\mu\gamma_\nu\gamma_\rho P_L u)$$
In the solution of the exercise they say that, from the Fierz identity:
$$(\bar{c}\gamma^\mu\gamma^\nu\gamma^\rho P_L b)(\bar{d}\gamma_\mu\gamma_\nu\gamma_\rho P_Lu)=16(\bar{c}\gamma^\mu P_L b)(\bar{d}\gamma_\mu P_L u)$$
How can I show that?