Ghost plasmon and negative dielectric function

We show explicitly that a negative value of the static dielectric function necessarily means the existence of what might be called a open-quotes ghost plasmon,close quotes a pole of the screened response χsc(q,ω) on the imaginary axis of ω. The ghost plasmon is a collective state exhausting most of the conductivity sum rule. This is demonstrated for a two-dimensional electron gas with a microscopic calculation. copyright 1997 The American Physical Society