= Solution
{c}
<Zero-point fields> are the irreducible <electromagnetic field> fluctuations in the <vacuum state>. Each <normal mode> has ground <energy> $\hbar\omega/2$. Although $\langle\mathcal E\rangle=\langle\mathcal B\rangle=0$ in the <vacuum state>, <3/d> gives $\langle\mathcal E^2\rangle=\langle\mathcal B^2\rangle=1$. These are quantum fluctuations, not a classical random coherent field with a known instantaneous value.
Two consequences are the <Lamb shift>, where coupling to the quantized <electromagnetic field> changes atomic <energy levels>, and <spontaneous emission>, where an excited <chemical atom> can emit a <photon> into an initially empty <normal mode>. In the latter process the <creation operator> has a nonzero <matrix element> $\langle1|a^\dagger|0\rangle=1$; stimulated-plus-spontaneous factors have the form $n+1$, which does not vanish at $n=0$. Descriptions splitting <spontaneous emission> into <vacuum fluctuations> and radiation reaction depend on operator-ordering conventions; the measurable total rate does not. <Zero-point fields> do not mean that the <vacuum state> contains a nonzero mean <photon number>.
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