Fierz identities with Majorana fermions in dim=4 and chirality

Question

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.

Answer 1

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.

Answer 2

The chiral matrix $\gamma^5$ can be defined using the epsilon tensor. See my answer to this post