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We calculate the influence of dynamical exchange effects on the response properties and the static properties of a two-dimensional many-polaron gas. These effects are not manifested in the random-phase approximation which is widely used in the analysis of the many-polaron system. Here they are taken into account by using a dielectric function derived in the time-dependent Hartree-Fock formalism. At weak electron-phonon coupling, we find that dynamical exchange effects lead to substantial corrections to the random-phase approximation results for the ground state energy, the effective mass, and the optical conductivity of the polaron system. Furthermore, we show that the reduction of the spectral weight of the optical absorption spectrum at frequencies above the longitudinal optical phonon frequency, due to many-body effects, is overestimated by the random-phase approximation. [ABSTRACT FROM AUTHOR]

Dynamical exchange interactions can be introduced in the dielectric function via a dynamic local field factor. We study the effects of this inclusion on both the static and the frequency dependent dielectric function of a two-dimensional electron gas, using the dynamic local field factor that we derived recently via the dynamical exchange decoupling method. The results are compared with the dielectric function in the Random Phase Approximation and with different dynamic and static approximations of the local field factor. [ABSTRACT FROM AUTHOR]