= Kramers-Kronig relations
{c}
{wiki=Kramers–Kronig_relations}
Causality constrains the real and imaginary parts of a frequency-dependent <linear response>. For a dielectric with $\epsilon_r(\omega)\to1$ at large frequency, the $e^{-i\omega t}$ convention gives
$$
\epsilon_r'(\omega)-1=\frac2\pi\operatorname{P}\int_0^\infty\frac{\omega'\epsilon_r''(\omega')}{\omega'^2-\omega^2}\,d\omega'.
$$
The integral is a <Cauchy principal value>. Absorption and <optical dispersion> therefore cannot be specified independently.
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