  We develop an extension of the Landau Fermi liquid theory to systems of
interacting fermions with non-trivial Berry curvature. We propose a kinetic
equation and a constitutive relation for the electromagnetic current that
together encode the linear response of such systems to external electromagnetic
perturbations, to leading and next-to-leading orders in the expansion over the
frequency and wave number of the perturbations. We analyze the Feynman diagrams
in a large class of interacting quantum field theories and show that, after
summing up all orders in perturbation theory, the current-current correlator
exactly matches with the result obtained from the kinetic theory.
