On the Relation between Optical Conductivity and Quasiparticle Dynamics:   Boson Structures
  An extended Drude form is often used to analyze optical data in terms of an optical scattering rate and renormalized mass corresponding, respectively, to the real and imaginary part of the memory function. We study the relationship between memory function and quasiparticle self energy for an isotropic system. We emphasize particularly boson signatures. We find it useful to introduce a new auxiliary model scattering rate and its Kramers-Kronig transform determined solely from optics which are much closer to the self energy than is the memory function itself in the normal state. In the superconducting state the simplification fails because the quasiparticle density of states acquires an essential energy dependence. 
J.P. Carbotte, E. Schachinger, and J. Hwang