Is there any function to have Fierz Identities for Majorana fermions in four dimensions?
Moreover, is there any method to split the chirality components of a fermion and implement the \gamma^5 matrix?
Thank you for your help.
For your first question: https://cadabra.science/notebooks/fierz.html (You just need to change the defined dimension from 11 to 4 at this notebook)
For your second question, I am curious about it too. Let me know if you can find a way to do that.
Have a good day.
The chiral matrix $\gamma^5$ can be defined using the epsilon tensor. See my answer to this post