Plasmon excitations in crystals

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Abstract
Using an analogy between the one-particle Green function G on the one hand and the dynamically screened electron-electron Coulomb interaction function W on the other for a many-electron system, we obtain a biorthonormal type of representation for the Fourier transform with respect to time of the function W. Based on the assumption that this function can be approximated in terms of simple poles in the complex energy plane, the connection between these poles and the energies of (damped) collective excitations, which are to be identified with plasmon excitations, is made clear. The biorthonormal-type representation of the screened interaction function W offers alternative computational prospects for the calculation of the electron self-energy in crystals.