In Peskin & Schroeder's QFT, how do you get from equation 2.35 to 2.37? (In particular, how does the invariant normalization of the Klein-Gordon real field imply that
$U(\Lambda)|p> = |\Lambda p>$ ?)

Also, on a more general note, could some explain why for the *real* Klein-Gordon field we need to make the effort to define invariant normalization? In particular, why do we care if the expression $<q|p>$ is invariant if it is $|<q|p>|^2$ which bears physical meaning?

This post imported from StackExchange Physics at 2014-07-13 04:43 (UCT), posted by SE-user PPR