# Total momentum operator for free scalar field

1. Aug 23, 2013

### 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 $a_{p}a_{-p}$ and $a_{p}^{\dagger}a_{-p}^{\dagger}$ Which I don't know how to get rid off, and shouldn't be in the final answer.

2. Aug 23, 2013

### Bill_K

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

3. Aug 23, 2013

### guillefix

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