Total momentum operator for free scalar field

[guillefix]

Sorry for reopening a closed thread. But I have exactly the same doubt as this guy: https://www.physicsforums.com/showthread.php?t=346730
And the answer doesn't actually answer his question. I do get delta(p+p'), but they just help me in getting [itex]a_{p}a_{-p}[/itex] and [itex]a_{p}^{\dagger}a_{-p}^{\dagger}[/itex] Which I don't know how to get rid off, and shouldn't be in the final answer.

 

[Bill_K]

You have at last to integrate over d³p. Your unwanted term is p a_p a_-p, and from the diametrically opposite value of p you'll get -p a_-p a_p. But the operators commute, so this is equivalently -p a_p a_-p, which cancels with the first term.

 

[guillefix]

Oh true, that's it! Thank you very much!