Trouble understanding a Peskin-Schroeder text

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praharmitra
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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 [tex]|0>[/tex] is to be invariant under translations, we must have

[tex]|0> = e^{i \textbf{P.x}} |0>[/tex].

How?!

2. How does
[tex]<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>[/tex].
?!

Thanks :)
 
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got it, thanks! :)