Sum rule for the optical absorption of an interacting many-polaron gas

A sum rule for the first frequency moment of the optical absorption of a ma ny-polaron system is derived, taking into account many-body effects in the system of constituent charge carriers of the many-polaron system. In our ex pression for the sum rule, the electron-phonon coupling and the many-body e ffects in the electron (or hole) system formally decouple, so that the many -body effects can be treated to the desired level of approximation by the c hoice of the dynamical structure factor of the electron (hole) gas. We calc ulate correction factors to take into account both low and high experimenta l cutoff frequencies.