I assume by "perfect conductor" you mean a material with zero resistance, or, which is the
same, infinite conductivity sigma.
I believe the imaginary part of the permittivity should diverge at zero frequency even for a
"non perfect" electrical conductor, i.e. a conductor with a finite...
well, my point is that:
Im eps = 4 pi sigma / omega
with eps(omega) = eps(omega,k-->0).
This means that for omega --> 0 then I am eps must diverge if sigma is finite, as it is in
metals. Or am I missing something ?
The imaginary part of the permittivity is related to the ratio between the optical conductivity and the frequency omega. So it would appear that in the limit omega --> 0
the imaginary part of the permittivity should diverge, for any metal with finite conductivity, right ?