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http://www.damtp.cam.ac.uk/user/tong/qft/two.pdf

Anyway [tex]\phi(\vec{x})[/tex] and [tex]\pi(\vec{x})[/tex] are given in equations 2.18 and 2.19

When I multiply out [itex]\pi(\vec{x}) \vec{\div} \phi(\vec{x})[/itex] I get four terms.

After normal ordering I can combine two of them to get the [tex]a_{\vec{p}}^\dagger a_{\vec{p}}[/tex] term I am meant to but I also have a [tex]a_{\vec{-p}} a_{\vec{p}}[/tex] and a [tex]a_{\vec{-p}}^\dagger a_{\vec{p}}^\dagger[/tex] term that I cannot get rid of.

Does anyone know how to get rid of the two extra terms?

Cheers