Causality, Kramers-Kronig Relations, and Landau Damping

ABSTRACT

We review the consequence of the causality in electrodynamics. The Kramers-Kronig relations are direct consequence of causality which has two ingredients: no perturbation in the remote past and irrelevance of future susceptibility to the present field. It is shown that the dielectric function obtained from the integration along the Landau contour can be derived from the Kramers-Kronig relations, thus the origin of the collisionless damping in plasmas is traced to the causality. An alternative derivation of the Kramers-Kronig relations based on the causal requirement is presented.

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