| We show that the solution of the Dyson equation for the electron-phonon (ep) problem considering the self-energy in the complex plane introduces important qualitative and quantitative effects compared to the widely considered quasi-particle expansion. We demonstrate the non trivial nature of the quasi-particle lifetime and dispersion relations as a function of the electron momentum. As a first and fundamental example, the Einstein model will be discussed. Bulk MgB2 will serve as a first-principle application to highlight the impact of our approach on the interpretation of ARPES experiments. Furthermore, we will discuss two-dimensional systems, where the ep coupling is very strong. |
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