Trouble understanding a Peskin-Schroeder text

[praharmitra]

I am having some trouble understanding the paragraph after eq (3.93) in Peskin Schroeder (Page 55). The chapter is on the Dirac Field. These are the parts where I am not following:

1. If the ground state $$|0>$$ is to be invariant under translations, we must have

$$|0> = e^{i \textbf{P.x}} |0>$$.

How?!

2. How does
$$<0| a^r_p {a^s_q}^\dagger e^{i P.x} |0>= e^{i(p-q).x} <0| e^{i P.x} a^r_p{a^s_q}^ \dagger |0>$$.
?!

Thanks :)

 

[praharmitra]

got it, thanks! :)