QFT: Proving Commutation of Fields & Momentum

[shadi_s10]

Hi everyone
My question is about QFT
I'm reading mandle and shaw
in chapter 2 as you know there is a question (2.4) about the commutations between the field and momentum.

[ [P]^{}[j], \phi ]

as momentum is in integral form I don't know how to prove them!

I tried to open the terms but I don't know how to put the field in an intergal!

 

[arkajad]

Call the x' integration variable in the definition of P. Calculate the commutator with phi(x) using the fact that integral is linear (much like a sum), therefore commutator with the integral is the integral of commutators. Use what you already know under the integral, simplify.