We study theoretically the quasiparticle lifetime, due to Coulomb scattering, in a two-dimensional electron system. It has long been established that in the limit of low excitation energy and temperature, the inverse lifetime behaves as ${\mathrm{\tau }}_{\mathrm{ee}}^{\mathrm{-}1}$(p)∝(Δ/${\mathrm{\epsilon }}_{\mathit{F}}$${)}^2$ln(${\mathrm{\epsilon }}_{\mathit{F}}$/Δ), where Δ≡max(|${\mathrm{\epsilon }}_{\mathit{p}}$-${\mathrm{\epsilon }}_{\mathit{F}}$|,${\mathit{k}}_{\mathit{BT}}$). This result has been obtained in the leading order of the Coulomb interaction. We show that higher-order terms in the interaction contribute higher-order logarithmic factors, meaning that a correct theory must sum up all orders of the interaction. After performing this summation, using the Keldysh diagram technique, we find that the renormalized lifetime still has the same general form as above. On the other hand we find that only forward scattering contributes to the lifetime, whereas, in leading-order theory, both forward and backward scattering make a contribution (a similar result has already been obtained for the two-dimensional Hubbard model). This leads to a different proportionality constant for the lifetime. Because we employ the Keldysh diagram technique, we are also able to give an expression for the collision operator, which can be used in the study of near-equilibrium processes. © 1996 The American Physical Society.

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