A QFT Field Expansion: Explaining (2.72) - Schwartz

[John Fennie]

The attached pic is from Schwartz.
Can someone explain the second equality sign in (2.72)?

 

[George Jones]

The attached pic is from Schwartz.
Can someone explain the second equality sign in (2.72)?

Use (2.69) and (2.71).

 

[John Fennie]

Use (2.69) and (2.71).

Hi that is my problem. I wasn't able to incorporate (2.69). Is there an idea?

 

[George Jones]

Rewrite (2.69) as
$$\left[ a_p , a_k^\dagger \right] = \left(2\pi\right)^3 \delta \left( \vec k - \vec p \right),$$
expand the left side, and use this in (2.72).

 

[John Fennie]

Rewrite (2.69) as
$$\left[ a_p , a_k^\dagger \right] = \left(2\pi\right)^3 \delta \left( \vec k - \vec p \right),$$
expand the left side, and use this in (2.72).

Thank you!