I have tried to understand paragraph 10.7 (Kallen-Lehmann Representation) in Weinberg's Quantum theory of fields (vol.1). He calculated matrix element
$$\langle0|\Phi(0)|p\rangle =(2\pi)^{-3/2}\left(2\sqrt{p^{2}+m^{2}}\right)^{-1/2}N.\tag{formula 10.7.19}$$
$N$ is constant. I can't understand how it was obtained. I don't even undestand why it depends on $p$. If we consider the Lorenz invariance of vacuum and operator $\Phi(0)$:
$$U_{\Lambda}|0\rangle=|0\rangle\ \ \text{ and } \ \ U_{\Lambda}\Phi(0)U_{\Lambda}^{-1}=\Phi(0)$$
then we have:
$$\langle0|\Phi(0)|p\rangle=\langle0|U_{\Lambda}^{\dagger}\Phi(0)|p\rangle=\langle0|U_{\Lambda}^{-1}\Phi(0)|p\rangle=\langle0|\Phi(0)U_{\Lambda}^{-1}|p\rangle=\langle0|\Phi(0)|U_{\Lambda}^{-1}p\rangle,$$
so
$$\langle0|\Phi(0)(p)=\langle0|\Phi(0)(U_{\Lambda}^{-1}p).$$
So my first guess was that this matrix element does not depend on $p$ and equals to constant.
Can you help me?