Calculation in Peskin&Schroeder QFT book

[aleazk]

Hi, i can't get the result stated as equation (2.33) in page 22. To be more clear, after the elimination of the divergent commutator, i still have two extra terms that i don't know how to cancel out. the total extra term is ap.a(-p)-a^+(-p).a^+p.

 

[dazhuzai8]

I think the extra terms are
$${\bf{P}}({a_{\bf{p}}}{a_{ - {\bf{p}}}} - {a^ + }_{ - {\bf{p}}}{a^ + }_{\bf{p}})$$
Notice that they are both odd function since a_p and a_(-p) are commute. Thus, the integration of them should be ZERO.