= Vacuum-to-one-particle scalar matrix element
{title2=$\langle\Omega|\phi(x)|p\rangle=F e^{-ip\cdot x}$}
For a massive spin-zero <one-particle state> with covariant normalization and a <Lorentz scalar> field, <Lorentz invariance> makes $F=\langle\Omega|\phi(0)|p\rangle$ independent of the on-shell <four-momentum> within a fixed species. A <Lorentz boost> to the <rest frame>, invariance of the <vacuum state> and scalar transformation at the origin prove this. <Translation covariance of a quantum field> then supplies the plane-wave factor. With noncovariant normalization, the boost law and the displayed momentum independence acquire energy factors.
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