# Non-abelian gauge theories, which factors commute?

I am following Peskin and Schroeder (1995). It seems that we are magically supposed to understand which factors commute and which do not in the theory. These are the factors which appear in the theories

• $\psi,\psi^a,\psi^a_L, \psi_L,\overline \psi,\overline \psi^a,\overline \psi_L,\overline \psi^a_L$
• $\phi, \phi^a$
• $\partial_\mu, \partial$
• $A_\mu, A^i, A^j_\mu$
• $B_\mu, B$
• $\gamma_\mu$
• $f^{abc}$
• $t^a, \tau^a, T^a$
• $k^\mu, k$

Which of these commute, and what is the rationale?

• Related post by OP: physics.stackexchange.com/q/369760/2451 – Qmechanic Nov 26 '17 at 18:58
• Can you narrow it to just a few passages you're confused about? The general rule is that matrices don't commute, numbers do. – knzhou Nov 26 '17 at 19:04