  Based on the Keldysh formalism, we derive an effective Boltzmann equation for
a quasi-particle associated with a particular Fermi surface in an interacting
Fermi liquid. This provides a many-body derivation of Berry curvatures in
electron dynamics with spin-orbit coupling, which has received much attention
in recent years in non-interacting models. As is well-known, the Berry
curvature in momentum space modifies naive band dynamics via an artificial
magnetic field in momentum space. Our Fermi liquid formulation completes the
reinvention of modified band dynamics by introducing in addition an "artificial
electric field", related to Berry curvature in frequency and momentum space. We
show explicitly how the artificial electric field affects the renormalization
factor and transverse conductivity of interacting U(1) Fermi liquids with
non-degenerate bands. Accordingly, we also propose a method of momentum
resolved Berry's curvature detection in terms of angle resolved photoemission
spectroscopy (ARPES).
