Question on peskin and schroeder

[HomogenousCow]

If you go to page 20 and 21 where the Fourier expansion of the klein-gordon field operator is derived, you'll see equation (2.27).
Now there are some small details of this whole calculation that I'm confused about.
I followed all the way through to (2.25), but here I feel a bit weird.
Isn't he trying to expand Φ(p)=(constant factor)(a+a* ) and plugging this back into the Fourier expression above (2.21)? However (2.27) directly contradicts this, instead he is taking Φ(p)=(constant factor)(a(p)+a*(-p) )
I understand that this is required to make the operator hermitian, but how is this formally justified step-by-step?
(Here I use * as a poor man's dagger)

 

[strangerep]

If you go to page 20 and 21 where the Fourier expansion of the klein-gordon field operator is derived, you'll see equation (2.27).
Now there are some small details of this whole calculation that I'm confused about.
I followed all the way through to (2.25), but here I feel a bit weird.

This step seems to confuse a lot of people (including me the first time I saw it). But it's actually really simple...

Isn't he trying to expand Φ(p)=(constant factor)(a+a* ) and plugging this back into the Fourier expression above (2.21)?

No.

However (2.27) directly contradicts this, instead he is taking Φ(p)=(constant factor)(a(p)+a*(-p) )
I understand that this is required to make the operator hermitian, but how is this formally justified step-by-step?

The expression in (2.25) is already hermitian. P&S simply perform a change of integration variable for the second term, i.e., $p \to -p$.

That's all it is.

(Here I use * as a poor man's dagger)

Try \dagger, e.g., $a^\dagger$. :D