Recent content by 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.

You should notice that {\gamma ^\mu }{\partial _\mu } = {\gamma ^0}{\partial _0} + {\bf{\gamma }} \cdot \nabla while {x^\mu }{y_\mu } = {g_{\mu \nu }}{x^\mu }{y^\nu } = {x^0}{y^0} - {\bf{x}} \cdot {\bf{y}} . There is no metric tensor in the four vector product \gamma^\mu \partial _\mu .