= Relativistic normalization of a one-particle state
{title2=$\langle\mathbf p|\mathbf q\rangle=2E_{\mathbf p}(2\pi)^3\delta^3(\mathbf p-\mathbf q)$}
If creation operators obey $[a_{\mathbf p},a^\dagger_{\mathbf q}]=(2\pi)^3\delta^3(\mathbf p-\mathbf q)$, set $|\mathbf p\rangle=\sqrt{2E_{\mathbf p}}a^\dagger_{\mathbf p}|0\rangle$. Their <inner product> then has the displayed value. The associated completeness measure is $d^3p/((2\pi)^3 2E_{\mathbf p})$, the invariant positive-energy <mass shell> measure. Specifying this normalization prevents hidden external energy factors in a <scattering amplitude>.
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